Anthony Pilkington scored the quickest Premier League goal of the season after 49 seconds to set Norwich on their way to victory against Swansea.
Russell Martin added his first top-flight goal before Danny Graham pulled one back for the visitors with his second of the season.
Pilkington scored a third midway through the second half to secure Norwich's third win in four games.
Swansea are still looking for a first away point after four matches.
Manager Brendan Rodgers had promised his Swansea side would produce a much more competitive performance away from the Liberty Stadium than on previous occasions this season, but they fell behind with less than a minute gone.
Elliott Bennett's looping cross from the right was headed down at the far post by the impressive Steve Morison and Pilkington thumped in a shot from close range.
Nine minutes later the lead was doubled when Martin was left unmarked to glance in David Fox's free-kick.
But the visitors halved the deficit within two minutes when Scott Sinclair burst into the area and, despite going down under Bennett's challenge, stabbed the ball across for Graham to score with a cross-shot.
Did you know?
- Norwich had only ever scored twice in the opening 10 minutes of a Premier League match once before - against Newcastle in 1994
Norwich continued to dominate, with Pilkington just missing from a narrow angle and Morison having a shot pushed wide by keeper Michel Vorm. Bennett also went close but his cross bounced off the bar just before the interval.
The tempo slowed dramatically after the break, though Sinclair came close to an equaliser with a low drive from 25 yards.
But from Fox's corner, Leon Barnett won a header and Bradley Johnson calmly lifted the ball across the box for Pilkington to score his second from close range.
Sinclair shot well over the bar from 30 yards to sum up Swansea's mounting frustration before Johnson forced a decent save from Vorm at the other end.
Grant Holt came off the bench for Norwich but was also denied by Vorm before Ashley Williams's sliding challenge stopped Wes Hoolahan getting a shot away from the rebound.
In a rare Swansea opening, substitute Stephen Dobbie shot straight at Marc Tierney before heading the follow-up straight to goalkeeper John Ruddy.
But otherwise Norwich's lead was never under real threat and Dobbie limped off with an ankle problem to leave Swansea to play the final minutes with 10 men.
After starting the season with two points from four matches, Norwich have now picked up nine from four games to move into the top half of the table.
Norwich manager Paul Lambert:
"I have been proud for the last two years with what the players have done and today we were excellent.
"Swansea came back at us after they got the goal back but the start we made was terrific and gave us something to build on. We were excellent in the second half.
"We've got to win more games than not and we're doing that at the moment."
Swansea manager Brendan Rodgers:
"We were disappointed to be 2-0 down before we even got going but the response and reaction to that was terrific.
"We've had four clean sheets and identified the threat at set-pieces from wide areas so to concede two of the goals from set-pieces is disappointing.
"The first year is very much about the home form and trying to pick up points away. We need to improve but the players are honest and one thing we've always done is bounce back."
Live Text Commentary
Full Time The referee ends the match.90:00 +4:03
Headed effort from inside the area by Leroy Lita misses to the left of the target.90:00 +3:24
Free kick awarded for an unfair challenge on Danny Graham by Marc Tierney. Direct free kick taken by Joe Allen.90:00 +3:02
Grant Holt gives away a free kick for an unfair challenge on Ashley Williams. Direct free kick taken by Leon Britton.88:34
Danny Graham produces a cross, Headed effort from inside the area by Leroy Lita misses to the right of the target.86:45
Outswinging corner taken from the right by-line by David Fox.78:13 Substitution
Substitution Wesley Hoolahan leaves the field to be replaced by Andrew Crofts.78:13
Elliott Bennett takes a shot from just outside the penalty area which clears the crossbar.77:11
Marc Tierney sends in a cross, clearance made by Ashley Williams.75:06
Stephen Dobbie takes a shot. Leon Barnett gets a block in.73:20 Substitution
Substitution Ashley Richards is brought on as a substitute for Neil Taylor.73:20
Stephen Dobbie produces a right-footed shot from just outside the box that misses to the right of the goal.71:52
Grant Holt takes a shot. Michel Vorm makes a save.69:51
Bradley Johnson takes a shot. Save by Michel Vorm.69:22
The ball is crossed by Kyle Naughton, Michel Vorm makes a save.68:22 Substitution
Substitution Leroy Lita on for Nathan Dyer.68:22
Shot by Scott Sinclair from outside the box goes over the net.66:18 Substitution
Substitution Grant Holt is brought on as a substitute for Steve Morison.64:34
Free kick awarded for an unfair challenge on Wesley Hoolahan by Ashley Williams. Indirect free kick taken by Bradley Johnson.64:19
Unfair challenge on Angel Rangel by Anthony Pilkington results in a free kick. Angel Rangel takes the free kick.
The assist for the goal came from Bradley Johnson.62:58 Goal scored
Goal! - Anthony Pilkington - Norwich 3 - 1 Swansea Anthony Pilkington finds the back of the net with a goal from inside the area to the bottom right corner of the goal. Norwich 3-1 Swansea.62:40
Corner taken by David Fox.59:47 Substitution
Substitution (Swansea) makes a substitution, with Stephen Dobbie coming on for Wayne Routledge.58:44
Corner taken right-footed by David Fox, Danny Graham makes a clearance.57:06
Scott Sinclair produces a right-footed shot from just outside the penalty box that misses to the left of the target.55:55
Shot by Anthony Pilkington from outside the area goes high over the crossbar.55:05
The ball is delivered by Bradley Johnson.54:53
The ball is sent over by Elliott Bennett.53:37
Nathan Dyer delivers the ball, blocked by Russell Martin.53:16
Foul by Russell Martin on Nathan Dyer, free kick awarded. Direct free kick taken by Ashley Williams.52:08
Elliott Bennett delivers the ball, clearance by Garry Monk.51:33
Bradley Johnson has an effort at goal from outside the penalty box missing to the wide right of the goal.51:05
Unfair challenge on Angel Rangel by Steve Morison results in a free kick. Angel Rangel takes the direct free kick.49:51
Inswinging corner taken by David Fox from the left by-line, Header from close range by Bradley Johnson misses to the right of the target.45:51
A cross is delivered by Anthony Pilkington, save by Michel Vorm.45:01
The referee starts the second half.45:00 +3:08 Half time
Half Time The ref blows to signal half-time.45:00 +1:35
The ball is delivered by Elliott Bennett. Danny Graham takes a shot. Blocked by Marc Tierney.43:13
The assistant referee signals for offside against Danny Graham. John Ruddy takes the indirect free kick.38:52
Centre by Anthony Pilkington.38:07
Nathan Dyer challenges Wesley Hoolahan unfairly and gives away a free kick. Direct free kick taken by John Ruddy.37:28
Inswinging corner taken right-footed by Joe Allen, clearance by Leon Barnett.37:08
Centre by Steve Morison, Angel Rangel manages to make a clearance.36:50
Anthony Pilkington produces a cross.36:10
Centre by Wayne Routledge, blocked by Russell Martin. Joe Allen takes the outswinging corner, Marc Tierney manages to make a clearance.34:52
Wesley Hoolahan concedes a free kick for a foul on Ashley Williams. Michel Vorm takes the direct free kick.33:47
Effort on goal by David Fox from outside the penalty box goes harmlessly over the bar.33:17
The ball is sent over by Elliott Bennett, blocked by Neil Taylor.32:05
Steve Morison takes a shot. Michel Vorm makes a save.30:41
Foul by Joe Allen on Marc Tierney, free kick awarded. Free kick taken by John Ruddy.29:21
Shot by Anthony Pilkington from deep inside the penalty area misses to the left of the target.28:22
Corner crossed in by Joe Allen, Marc Tierney manages to make a clearance.25:37
Scott Sinclair takes a shot. Leon Barnett gets a block in.24:47
Neil Taylor produces a cross. Effort from just outside the area by Angel Rangel goes over the target.24:38
Centre by Neil Taylor.22:22
Steve Morison produces a right-footed shot from just outside the penalty box that misses to the left of the target.19:38
Anthony Pilkington takes a shot. Angel Rangel gets a block in.17:17
Danny Graham is caught offside. Free kick taken by John Ruddy.12:53
The ball is sent over by Nathan Dyer, blocked by Leon Barnett. Joe Allen decides to take a short corner. Shot by Angel Rangel. Anthony Pilkington gets a block in.12:33
Wayne Routledge sends in a cross, blocked by David Fox.11:18
Assist on the goal came from Scott Sinclair.11:18 Goal scored
Goal! - Danny Graham - Norwich 2 - 1 Swansea Danny Graham finds the net with a goal from inside the six-yard box to the bottom right corner of the goal. Norwich 2-1 Swansea.9:15
David Fox provided the assist for the goal.9:15 Goal scored
Goal! - Russell Martin - Norwich 2 - 0 Swansea Russell Martin finds the net with a headed goal from inside the area. Norwich 2-0 Swansea.8:29
Anthony Pilkington fouled by Angel Rangel, the ref awards a free kick. David Fox produces a cross,6:58
Wayne Routledge takes a shot. Save made by John Ruddy. Steve Morison produces a cross.4:17
The ball is delivered by Elliott Bennett, Ashley Williams manages to make a clearance.3:30
David Fox takes the direct free kick.3:30 Booking
Booking Garry Monk shown a yellow card.3:16
Garry Monk concedes a free kick for a foul on Steve Morison.0:56
The ball is swung over by Kyle Naughton.0:51
Assist on the goal came from Steve Morison.0:51 Goal scored
Goal! - Anthony Pilkington - Norwich 1 - 0 Swansea A goal is scored by Anthony Pilkington from inside the penalty box low into the middle of the goal. Norwich 1-0 Swansea.0:39
David Fox takes a shot. Garry Monk gets a block in.0:00
The referee gets the game started.
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