Santi Cazorla hit Arsenal's 50th league goal of the season to earn Arsene Wenger's 10 men a victory that lifted them to fifth spot in the table.
The Spanish forward fired through a sea of Sunderland legs after good work by Theo Walcott, before Carl Jenkinson was sent off for two bookable offences.
Arsenal were forced to endure some nervous moments, Steven Fletcher and Titus Bramble both wasting chances.
Walcott hit the post for Arsenal, who lost Jack Wilshere to injury.
Wenger will hope England international Wilshere, who limped off early in the second half, makes a speedy recovery. The Gunners struggled after the 21-year-old left the field before confirming a third win in four league games.
Wenger's side were forced to dig deep to secure the points with Wojciech Szczesny producing a flurry of late saves to keep out Fletcher, Stephane Sessegnon and Adam Johnson.
The tone for a hard-fought encounter was set inside the opening 10 minutes.
The Black Cats welcomed back captain Lee Cattermole from a knee injury for his first league start since November and the midfielder was cautioned inside two minutes for a late challenge on Aaron Ramsey, before Jenkinson saw yellow for a lunge on Jack Colback.
Jenkinson was only starting because French defender Laurent Koscielny tweaked his calf in the warm-up, Bacary Sagna moving to the centre of defence.
What a thriller. Arsenal appeared to be coasting until they lost Jack Wilshere to injury and then Carl Jenkinson to a red card. Martin O'Neill will spend the rest of the weekend, and beyond, wondering how on earth his Sunderland side did not find the net
Sagna endured a couple of nervous moments before the Gunners seized control through Cazorla's 35th-minute goal, a well executed finish from 15 yards through a sea of legs following a delightful move involving Walcott.
Wenger's side were playing with confidence and authority.
When the teams met in north London on the opening weekend of the season, the Gunners had 23 shots without scoring and they suffered further frustration as Simon Mignolet single-handedly kept the Black Cats in the game in the first half.
The Belgian goalkeeper had already produced a flying save to keep out Ramsey's curling 20-yard attempt before Cazorla's goal. Then Mignolet spread himself to prevent the Wales international from making it 2-0 at the end of the first half.
If the loss of Wilshere in the 50th minute was a setback for the visitors, then the red card flashed by referee Anthony Taylor in the direction of Jenkinson, who celebrated his 21st birthday on Friday, was a blow.
The former Charlton player could hardly complain, however, after a clumsy challenge on Sessegnon brought his second yellow card.
Suddenly it was all Sunderland. Fletcher blazed a chance wide after Sessegnon had dispossessed Ramsey and Szczesny then denied the former Wolves striker.
Bramble somehow failed to score from close range in front of a gaping net, while at the other end Walcott hit the post with a low finish following a wonderfully weighted pass by the impressive Cazorla.
There was still time for Adam Johnson to force another save from Szczesny but Sunderland, for all their determination and effort, could find no way through.
Sunderland manager Martin O'Neill:
"It was a great game from start to finish. The tempo was very high early on and it remained so.
"Obviously Arsenal, a top-quality team, caused us a lot of problems in the first half but I also thought we looked dangerous as well.
"But in the second half, we just came roaring at them, and that was even before the man had been sent off.
"Seriously, looking back at a couple of the chances, I just don't know how we didn't score."
Arsenal manager Arsene Wenger:
"It was tight in the end, but it was a game with a high level of intensity where we have shown some brilliance going forward, but unfortunately we couldn't score the second goal.
"Then we had to show another side in the second half, especially in the last 20 minutes, down to 10 men, we needed to be resilient, committed and deal with everything they offered us.
"But overall, I think it was a typical Premier League game with top quality on both sides."
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Live Text Commentary
Full Time The game is over, as the referee blows his whistle.90:00 +3:53
Craig Gardner crosses the ball, clearance by Bacary Sagna. Inswinging corner taken right-footed by Sebastian Larsson from the left by-line.90:00 +3:19
Shot from deep inside the area by Santi Cazorla clears the bar.90:00 +2:10
Shot from just outside the box by Olivier Giroud goes over the bar.90:00 +1:55
Stephane Sessegnon sends in a cross, clearance by Vassiriki Diaby.90:00 +1:41
The ball is sent over by Adam Johnson, Bacary Sagna makes a clearance.90:00 +1:20
Sebastian Larsson takes a inswinging corner from the left by-line to the near post, Olivier Giroud makes a clearance.90:00 +1:05
Sebastian Larsson takes a inswinging corner to the near post, Vassiriki Diaby makes a clearance.90:00 +0:50
Adam Johnson takes a shot from 25 yards. Save made by Wojciech Szczesny.89:48
Free kick awarded for an unfair challenge on Mikel Arteta by David Vaughan. Wojciech Szczesny restarts play with the free kick.89:32
The ball is swung over by Adam Johnson, Bacary Sagna manages to make a clearance.89:17
Shot from 25 yards by Craig Gardner. Clearance made by Bacary Sagna.88:21
Mikel Arteta takes a short corner.88:07
Aaron Ramsey produces a cross, clearance made by Titus Bramble.86:59
David Vaughan has an effort at goal from outside the penalty box missing to the wide left of the goal.86:52
Adam Johnson crosses the ball, clearance by Mikel Arteta.85:56
Direct free kick taken by Sebastian Larsson.85:56 Substitution
Substitution Theo Walcott leaves the field to be replaced by Ignasi Miquel.85:56
Free kick awarded for a foul by Mikel Arteta on Danny Graham.84:41
Steven Fletcher takes a shot. Wojciech Szczesny makes a save. Corner from the right by-line taken by Adam Johnson, Titus Bramble has an effort at goal from close range which goes wide left of the target.
Inswinging corner taken right-footed by Sebastian Larsson from the left by-line to the near post, clearance by Aaron Ramsey.84:01
A cross is delivered by David Vaughan, clearance made by Vassiriki Diaby.83:03
Free kick crossed by Sebastian Larsson.83:03 Booking
Booking Theo Walcott is cautioned by the ref for unsporting behaviour.82:53
Free kick awarded for an unfair challenge on Stephane Sessegnon by Theo Walcott.81:42
The assistant referee flags for offside against Craig Gardner. Wojciech Szczesny restarts play with the free kick.81:11 Substitution
Substitution David Vaughan joins the action as a substitute, replacing Danny Rose.80:59
Craig Gardner produces a drilled right-footed shot from 25 yards. Blocked by Per Mertesacker.80:48
The ball is delivered by Craig Gardner.78:22
The ball is swung over by Danny Rose, clearance made by Per Mertesacker.77:47
Craig Gardner crosses the ball, save by Wojciech Szczesny.77:17
Steven Fletcher takes a shot. Save made by Wojciech Szczesny.76:48
The assistant referee flags for offside against Theo Walcott. Simon Mignolet restarts play with the free kick.75:17 Booking
Booking Booking for Jack Colback for unsporting behaviour.74:07
Effort from inside the area by Theo Walcott strikes the post.73:26
Santi Cazorla takes a shot from just inside the penalty box which clears the bar.72:56
The ball is sent over by Sebastian Larsson, save made by Wojciech Szczesny.72:42
Centre by Sebastian Larsson, clearance made by Aaron Ramsey.72:14
Sebastian Larsson takes a inswinging corner from the left by-line to the near post, Olivier Giroud manages to make a clearance.70:36
Adam Johnson takes a corner.70:30
Stephane Sessegnon delivers the ball.68:44
Vassiriki Diaby takes a shot. Comfortable save by Simon Mignolet.68:20
Santi Cazorla has an effort at goal. John O'Shea gets a block in.67:21
Wojciech Szczesny takes the indirect free kick.67:21 Substitution
Substitution Danny Graham comes on in place of Alfred N'Diaye.67:21
The assistant referee signals for offside against Steven Fletcher.66:48
Inswinging corner taken left-footed by Adam Johnson from the right by-line, Nacho Monreal manages to make a clearance.66:38
The ball is sent over by Craig Gardner.65:02
Effort from the edge of the area by Olivier Giroud goes wide of the left-hand post.63:38
Theo Walcott challenges Danny Rose unfairly and gives away a free kick. Direct free kick taken by Simon Mignolet.63:07
Direct free kick taken by Wojciech Szczesny.63:07 Booking
Booking The referee shows Sebastian Larsson a yellow card.62:58
Unfair challenge on Santi Cazorla by Titus Bramble results in a free kick.61:52
The free kick is swung in right-footed by Sebastian Larsson, clearance made by Mikel Arteta.61:52 Dismissal
Dismissal Red card for Carl Jenkinson.61:45
Carl Jenkinson concedes a free kick for a foul on Stephane Sessegnon.60:39
Santi Cazorla has an effort at goal from deep inside the area missing to the right of the target.57:48
Steven Fletcher produces a drilled left-footed shot from deep inside the penalty box which goes wide of the left-hand post.56:06
Corner taken by Adam Johnson from the right by-line played to the near post.55:14
Olivier Giroud has an effort at goal from the edge of the box that misses to the right of the target.55:08
Centre by Olivier Giroud, clearance by Danny Rose.53:40
Sebastian Larsson challenges Mikel Arteta unfairly and gives away a free kick. Mikel Arteta restarts play with the free kick.52:45
Danny Rose sends in a cross, Bacary Sagna makes a clearance.52:27
Shot by Stephane Sessegnon. Blocked by Mikel Arteta.51:59
Adam Johnson takes the inswinging corner, Vassiriki Diaby manages to make a clearance.51:19
Foul by Aaron Ramsey on Danny Rose, free kick awarded. Sebastian Larsson delivers the ball from the free kick right-footed from left wing, clearance made by Per Mertesacker.48:37
Free kick taken by Santi Cazorla.48:37 Substitution
Substitution Vassiriki Diaby on for Jack Wilshere.48:37
Alfred N'Diaye concedes a free kick for a foul on Jack Wilshere.45:01
The second half begins.45:01 Substitution
Substitution (Sunderland) makes a substitution, with Sebastian Larsson coming on for Lee Cattermole.45:00 +1:24 Half time
Half Time The match has reached half-time.45:00 +0:41
Aaron Ramsey takes a shot. Save made by Simon Mignolet. Steven Fletcher is caught offside. Wojciech Szczesny restarts play with the free kick.44:32
Free kick awarded for an unfair challenge on Lee Cattermole by Olivier Giroud. Simon Mignolet takes the direct free kick.44:22
The ball is crossed by Olivier Giroud, Craig Gardner gets a block in.43:35
Shot by Theo Walcott. Save by Simon Mignolet.43:25
The ball is crossed by Nacho Monreal, clearance by Titus Bramble.42:12
Theo Walcott has an effort at goal from just inside the box that misses to the left of the target.40:30
The ball is delivered by Danny Rose, save by Wojciech Szczesny.38:21
Jack Wilshere sends in a cross, clearance by Danny Rose. Corner taken by Jack Wilshere from the right by-line, clearance made by Titus Bramble.34:59
Theo Walcott provided the assist for the goal.34:59 Goal scored
Goal! - Santi Cazorla - Sunderland 0 - 1 Arsenal Santi Cazorla grabs a goal from just inside the penalty area to the bottom right corner of the goal. Sunderland 0-1 Arsenal.31:35
Shot by Aaron Ramsey from 20 yards. Save made by Simon Mignolet.31:07
A cross is delivered by Craig Gardner, clearance by Bacary Sagna.29:51
The ball is delivered by Craig Gardner.27:31
Centre by Aaron Ramsey, clearance by John O'Shea.26:11
The ball is sent over by Adam Johnson.25:27
The offside flag is raised against Craig Gardner. Per Mertesacker restarts play with the free kick.22:16
Stephane Sessegnon takes a shot from long range which goes wide of the right-hand post.21:16
Lee Cattermole fouled by Jack Wilshere, the ref awards a free kick. Free kick taken by Titus Bramble.18:29
The official flags Adam Johnson offside. Wojciech Szczesny restarts play with the free kick.17:32
Free kick awarded for a foul by Mikel Arteta on Steven Fletcher. Direct free kick taken by Craig Gardner.16:59
Effort on goal by Olivier Giroud from deep inside the penalty area misses to the right of the goal.16:11
Steven Fletcher takes a shot. Wojciech Szczesny makes a comfortable save.15:50
Free kick awarded for an unfair challenge on Stephane Sessegnon by Nacho Monreal. Craig Gardner restarts play with the free kick.15:08
Centre by Stephane Sessegnon, Carl Jenkinson makes a clearance.13:05
Free kick awarded for a foul by Carl Jenkinson on Steven Fletcher. Danny Rose takes the direct free kick.12:47
Effort on goal by Olivier Giroud from 20 yards. Save made by Simon Mignolet.10:40
Jack Colback delivers the ball, Per Mertesacker makes a clearance.9:49
Lee Cattermole fouled by Aaron Ramsey, the ref awards a free kick. Simon Mignolet takes the direct free kick.9:19
Alfred N'Diaye concedes a free kick for a foul on Mikel Arteta. Per Mertesacker restarts play with the free kick.8:20
Free kick crossed by Craig Gardner, Wojciech Szczesny makes a comfortable save.8:20 Booking
Booking Carl Jenkinson receives a caution for unsporting behaviour.7:58
Foul by Carl Jenkinson on Jack Colback, free kick awarded.6:46
Mikel Arteta challenges Alfred N'Diaye unfairly and gives away a free kick. John O'Shea takes the direct free kick.4:27
Free kick awarded for a foul by Lee Cattermole on Jack Wilshere. Aaron Ramsey takes the free kick.3:32
Theo Walcott takes a shot. Simon Mignolet makes a save.2:04
Corner taken by Craig Gardner from the left by-line played to the near post.1:28 Booking
Booking Booking for Lee Cattermole for unsporting behaviour.1:10
Shot by Theo Walcott. Save by Simon Mignolet.0:27
The ball is delivered by Craig Gardner, Alfred N'Diaye has a header from close range and clears the crossbar.0:00
The game begins.
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