Frank Lampard's early goal saw Chelsea slow Sunderland's resurgence under Martin O'Neill despite a nervy finale.
Lampard reacted quickly to bundle the ball home from close range after a breathtaking volley from Fernando Torres crashed back off the bar.
Torres, Lampard and Juan Mata all had chances to add to the lead.
But Sunderland created as many openings as their hosts and will particularly rue two glorious late chances missed by Craig Gardner and Nicklas Bendtner.
Substitute Gardner was the bigger culprit, shooting wastefully wide with a first-time effort from 12 yards after a brilliant run and pull-back by Sebastian Larsson.
But Bendtner should have done better, chipping an effort high and wide in injury time.
James McClean also miskicked when well placed in the second half but Chelsea, who were able to bring on fit-again midfielder Michael Essien as a late substitute, rode their luck to see out the win and close the gap to third-placed Tottenham to six points .
Sunderland played with purpose and quality and will feel aggrieved to leave Stamford Bridge with nothing after an impressive second half.
Having won five of their seven matches under O'Neill, they started promisingly and were only denied what appeared a certain goal early on by a brilliant piece of defending by Jose Bosingwa.
The Portuguese came in for some fierce criticism for a less than inspiring defensive display in the win at Wolves, but he did superbly to dart in front of McClean and prevent a free shot at goal from eight yards after a brilliant, bustling run by Stephane Sessegnon.
Sessegnon was the key man for the Black Cats and was a constant menace to the home defence, operating just behind lone striker Bendtner.
But it was Chelsea's creative dynamo Mata who turned in yet another decisive performance to add to an ever-growing list.
Mata played the telling pass for Lampard's opener after some wonderful, patient build-up play that involved both full-backs and all of the Chelsea midfield and attack.
I don't think Chelsea can win the league. I think they are too far adrift and are not a good enough side. Fernando Torres is beginning to look the part but luck has deserted him and he has now gone 14-and-a-half hours without scoring a goal for club or country.
Raul Meireles saw his initial strike blocked, but the Blues retained possession and Mata's dinked cross to the far post was acrobatically volleyed against the bar by Torres, and Lampard somewhat fortuitously managed to knock the ball over the line.
Spaniard Mata also saw a fine long-range free-kick saved in the first half and his trickery and ability to pick a final pass always seemed likely to provide a second home goal.
Torres, buoyed by his early contribution, fired a low shot just wide and then his goalbound header was cleared by the backpedalling Phil Bardsley.
Lampard also had a volleyed attempt blocked as Chelsea looked to settle the game before the break.
But the Black Cats responded in style and Bendtner was very unlucky to drift a low shot past the post after a fine pass from Sessegnon.
And Sunderland got on top after the interval.
David Vaughan fizzed a fine shot narrowly past the post and Bendtner had a strong shout for a penalty ignored by referee Phil Dowd after going down in the box following a heavy challenge by Ashley Cole.
Torres also had two worthy Chelsea claims for spot-kicks turned down - the second of which saw him harshly booked for diving - while Meireles went close with a deft chip.
Essien came off the bench after six months out with a knee injury to lift the home crowd with 15 minutes remaining.
However Chelsea, who should have Gary Cahill in their ranks for next Saturday's game against Norwich at Carrow Road , were looking increasingly shaky and the visitors should have claimed a point.
But they lacked the composure to take advantage of the home side's frailties, squandering the three superb chances they created in the closing stages.
Chelsea manager Andre Villas-Boas
"In the first half we were always in control. We were the better team and created a lot of chances. In the second half it was split in terms of chances and there were big, big chances for both sides.
"Sunderland created their opportunities and we, on the counter attack, created ours. Both teams had good opportunities and it could have gone 2-0 or 1-1.
"To break the run of form of Sunderland is good and with the other results it was a good three points. It was a good team performance.
"Although we were under pressure we managed to keep our shape and our discipline to hold on to an important result. We were solid and competitive and dominant in the first half.
"Fernando Torres is getting his good run of games, finding inspiration, finding motivation, finding form. He has all the team behind him and the fans behind him."
Sunderland manager Martin O'Neill:
"We had a fantastic second half. We created a number of clear-cut chances and we weren't able to take just one of them. We are wondering how on earth we lost the game.
"With a bit of composure we could have scored four goals. We had enough chances to have won three games. And we had a clear-cut penalty.
"We played very, very well and it wasn't just a case of just putting a big effort into the game. We played very well, played very nice football.
"The performance was excellent and we can take some consolation from the fact the fans were screaming for the final whistle."
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +2:13
Nicklas Bendtner produces a left-footed shot from deep inside the penalty box which goes wide of the left-hand upright.89:51
Florent Malouda takes a shot. Save by Simon Mignolet.89:10
Effort from deep inside the area by Craig Gardner misses to the right of the target.88:45
The ball is delivered by Ramires, blocked by John O'Shea.87:54
Shot on goal by Raul Meireles from inside the box goes harmlessly over the target.87:04
Raul Meireles takes a outswinging corner.86:02
James McClean sends in a cross, save by Petr Cech.85:05
Raul Meireles has a lobbed shot. Simon Mignolet makes a save. Outswinging corner taken right-footed by Raul Meireles from the right by-line.84:16 Substitution
Substitution Florent Malouda on for Juan Mata.83:16
Sebastian Larsson produces a cross, clearance made by David Luiz.82:58
The ball is delivered by James McClean, John Terry makes a clearance.82:43
Centre by James McClean.80:52
A cross is delivered by James McClean, clearance by John Terry. Inswinging corner taken right-footed by Sebastian Larsson from the left by-line, Petr Cech makes a save.79:56 Substitution
Substitution Connor Wickham is brought on as a substitute for Kieran Richardson.79:32
Michael Essien is caught offside. Simon Mignolet restarts play with the free kick.79:01
Corner taken right-footed by Raul Meireles, Phillip Bardsley manages to make a clearance.77:29
The ball is sent over by Raul Meireles, clearance by Phillip Bardsley.76:45
Juan Mata produces a left-footed shot from the edge of the box and misses to the right of the goal.74:58
Raul Meireles fouled by Lee Cattermole, the ref awards a free kick. Michael Essien restarts play with the free kick.
Michael Essien takes a shot and missed to the left of the target.72:32
Free kick taken by John O'Shea.72:32 Substitution
Substitution (Chelsea) makes a substitution, with Michael Essien coming on for Frank Lampard.72:32 Booking
Booking Caution for Raul Meireles.72:17
Foul by Raul Meireles on Sebastian Larsson, free kick awarded.70:05
Ramires fouled by Michael Turner, the ref awards a free kick. Juan Mata has a direct shot on goal from the free kick.68:24
Simon Mignolet takes the free kick.68:24 Substitution
Substitution Craig Gardner on for David Vaughan.68:24
The assistant referee signals for offside against Juan Mata.66:43
Centre by Phillip Bardsley, clearance by David Luiz.65:25 Booking
Booking Fernando Torres is cautioned by the ref for unsporting behaviour.64:13
Foul by Lee Cattermole on Frank Lampard, free kick awarded. Frank Lampard produces a shot on goal direct from the free kick.63:08
James McClean produces a left-footed shot from close in which goes wide of the left-hand upright.62:30
The ball is swung over by James McClean, save made by Petr Cech.62:10
Kieran Richardson takes a shot. Raul Meireles gets a block in.61:14
Free kick awarded for a foul by Frank Lampard on Stephane Sessegnon. Free kick crossed by Sebastian Larsson, Jose Bosingwa manages to make a clearance.58:48
David Vaughan takes the chance to get an effort at goal and missed to the right of the net.57:15
Frank Lampard takes the direct free kick.57:15 Booking
Booking Lee Cattermole goes into the book for unsporting behaviour.57:03
Lee Cattermole gives away a free kick for an unfair challenge on Frank Lampard.55:15
Centre by Ashley Cole.54:55
Phillip Bardsley sends in a cross, save made by Petr Cech.51:26
Frank Lampard takes the inswinging corner, Juan Mata has an effort at goal from close in which goes wide of the left-hand upright.50:39
Fernando Torres takes a shot. Save by Simon Mignolet. Corner from the right by-line taken by Juan Mata, John O'Shea makes a clearance.49:47
Free kick awarded for a foul by Jose Bosingwa on Kieran Richardson. Free kick taken by Simon Mignolet.46:47
Stephane Sessegnon takes a shot. Save made by Petr Cech.45:16
Free kick awarded for a foul by Jose Bosingwa on Nicklas Bendtner. Direct free kick taken by David Vaughan.45:01
The referee starts the second half.45:00 +3:29 Half time
Half Time The players leave the pitch at half time.45:00 +1:37
Free kick awarded for a foul by Nicklas Bendtner on Oriol Romeu. Free kick taken by John Terry.45:00 +0:50
Unfair challenge on John O'Shea by Oriol Romeu results in a free kick. Michael Turner takes the direct free kick.45:00 +0:04 Substitution
Substitution Michael Turner joins the action as a substitute, replacing Matthew Kilgallon.40:25
Phillip Bardsley concedes a free kick for a foul on Fernando Torres. Free kick taken by Ashley Cole.39:34
The referee penalises Jose Bosingwa for handball. Free kick crossed by Sebastian Larsson, save by Petr Cech.38:43
Fernando Torres has an effort at goal from outside the penalty box which goes wide left of the goal.34:39
Nicklas Bendtner has an effort at goal from deep inside the area missing to the left of the goal.33:16
The ball is crossed by Nicklas Bendtner, clearance made by Ashley Cole. Inswinging corner taken by David Vaughan.30:18
The ball is crossed by Ramires, Fernando Torres takes a shot. Blocked by Matthew Kilgallon.27:10
Free kick awarded for a foul by Frank Lampard on Phillip Bardsley. Phillip Bardsley restarts play with the free kick.25:49
Unfair challenge on David Luiz by David Vaughan results in a free kick. Direct effort from the free kick comes in from Juan Mata, save made by Simon Mignolet.24:51
Shot from long distance by David Luiz goes wide of the left-hand upright.24:36
Juan Mata takes a shot. Blocked by Frank Lampard.21:10
Lee Cattermole concedes a free kick for a foul on Frank Lampard. Direct free kick taken by John Terry.18:58
David Vaughan fouled by Fernando Torres, the ref awards a free kick. Phillip Bardsley takes the free kick.16:14
Corner from the left by-line taken by Juan Mata, Frank Lampard takes a shot. Clearance by Sebastian Larsson. Corner taken left-footed by Juan Mata from the left by-line, clearance made by Matthew Kilgallon.15:29
Nicklas Bendtner takes a shot. Save by Petr Cech.14:21
Unfair challenge on Phillip Bardsley by Oriol Romeu results in a free kick. John O'Shea restarts play with the free kick.12:25
Assist by Fernando Torres.12:25 Goal scored
Goal! - Frank Lampard - Chelsea 1 - 0 Sunderland Frank Lampard scores a goal from inside the six-yard box to the bottom left corner of the goal. Chelsea 1-0 Sunderland.12:20
Fernando Torres takes a shot.11:55
Shot by Raul Meireles. Blocked by John O'Shea.10:09
Headed effort from inside the area by Fernando Torres misses to the right of the target.7:38
Direct effort from the free kick comes in from Sebastian Larsson, save made by Petr Cech.7:38 Booking
Booking Booking for David Luiz.7:32
David Luiz challenges Nicklas Bendtner unfairly and gives away a free kick.5:27
Nicklas Bendtner gives away a free kick for an unfair challenge on Ashley Cole. Fernando Torres takes the direct free kick.4:02
Corner from the right by-line taken by Juan Mata, Frank Lampard takes a shot. Phillip Bardsley gets a block in. Header on goal by Frank Lampard from inside the box goes harmlessly over the target.0:00
The referee gets the game started.
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