A scintillating Scott Sinclair hat-trick fired Swansea through to the fourth round of the Carling Cup.
Stephen Dobbie set him on a weaving run and Sinclair's shot was too strong for Joe Lewis' parry, but Charlie Lee fed Craig Mackail-Smith for the equaliser.
Sinclair again showed finishing prowess after David Cotterill's slick pass.
Mackail-Smith missed an open goal for Peterborough, Swansea hitting straight back as Dobbie's audacious back-heel let Sinclair slide the ball past Lewis.
It is just the second time in 33 years that Swansea have reached the fourth round, and they will hope for a glamour tie when the draw is made on Saturday.
The south Wales club have reached the last 16 three times, but have never been beyond that.
The defeat ended Posh's 100% record at London Road this season, where they had won five-out-of-five matches, scoring 18 goals.
Former Chelsea winger Sinclair was a constant thorn in the side of the Peterborough defence, and tested former England Under-21 international goalkeeper Lewis after just two minutes.
The Swansea youngster, who Swansea manager Brendan Rodgers has championed for an England U21 call-up, cut inside and unleashed a 20-yard shot that Lewis punched clear.
Stephen Dobbie (centre) set up Scott Sinclair (right) for two goals
But three minutes later the visitors were ahead when Sinclair danced through the Peterborough defence before his shot was deflected into the net via Lewis and defender Gabriel Zakuani.
The lead lasted just 60 seconds, though, as Peterborough unlocked the makeshift Swansea defence with ease.
Lee sped into the penalty area before crossing for the unmarked Mackail-Smith to drill home the equaliser.
The League One pace-setters were unlucky not to go in front two minutes later when George Boyd's pass found Aaron McLean in space on the edge of the six-yard box, but new Swansea keeper Yves Makabu-Makalambay saved superbly.
In the 37th minute Sinclair brought another fine save from Lewis with a curling shot before he latched on to Cotterill's delightfully threaded through-ball to put the visitors back in front four minutes later.
Peterborough felt they were unlucky not to have two penalties, but referee Nigel Miller rejected their appeals.
The official was at the centre of much controversy throughout the second half by failing to award clear free kicks to both sides.
Swansea should have put the game beyond Posh's reach on the hour, but Dobbie missed from six yards - a misdemeanour repeated by Sinclair in the 75th minute.
Sandwiched in between those misses were two close efforts from Peterborough.
First Boyd sent a shot just wide of the right-hand upright and then, in the 73rd minute, substitute Lee Tomlin brought a fine save from Makabu-Makalambay - only for referee Miller to award a goal-kick.
But Peterborough's miserable night was completed inside two minutes.
In the 76th minute, Tomlin supplied a superb cross for Mackail-Smith, but the Posh striker somehow contrived to fire over the bar from two yards out.
The miss was punished almost immediately when Joe Allen's build-up work and Dobbie's outrageous piece of skill put Sinclair through on goal and the winger picked his spot from six yards for his seventh goal since moving to Swansea in the summer.
That killed off Peterborough's resistance, their final chance coming to naught when Mackail-Smith was again denied by Makabu-Makalambay.
"Sinclair is still blossoming," said Swansea manager Brendan Rodgers, who worked with the winger in the Chelsea youth set-up. "He gets better with games and is really maturing.
"He was a big talent when he broke on the scene at 17 but then went out on loan at teams where he did not play.
"He needed to find a home. I spent hours on the phone to him and convinced him that Swansea was the place for him to be. He can help the club and help himself.
"He has had two years resting. He is so fresh, he wants to play every game. He wants to score goals and at this moment in time in his career, he will tell you, he wants to play football."
Posh boss Gary Johnson was unhappy with referee Miller who refused to give the home side a penalty, despite numerous appeals.
"We are angry," said Johnson. "It spoilt the game because I don't think he wanted to make those kind of decisions.
"If it was once or twice, you might be unlucky, but you are not unlucky five times.
"I felt we didn't quite finish the game well enough. The last 20 minutes, we were demoralised."
Live text and stats
Tuesday, 21 September 2010
22 Ofori-Twumasi (Davies 86)
18 Whelpdale (Tomlin 56 yellow card)
19 Mendez-Laing (Hibbert 70)
08 Pratley yellow card
11 Van der Gun (Allen 70)
15 Lopez (Gower 66)
21 Sinclair (Dyer 81)
Ref: MillerAtt: 4,164
Attempts on target
Attempts off target
90:00+4:15 The referee brings the game to a close.
90:00+3:35 Craig Mackail-Smith takes a shot. Save by Yves Ma-Kalambay.
89:26 Free kick awarded for a foul by Joe Allen on Charlie Lee. Direct free kick taken by George Boyd.
85:42 Short corner taken by David Cotterill from the right by-line.
85:27 Substitution Jay Davies on for Seth Nana Ofori-Twumasi.
85:07 Stephen Dobbie takes a shot. Save by Joe Lewis.
84:43 Aaron Mclean sends in a cross.
84:18 David Cotterill has shot on goal from just outside the penalty box which goes wide of the right-hand upright.
80:56 Substitution Nathan Dyer is brought on as a substitute for Scott Sinclair.
80:46 Scott Sinclair produces a right-footed shot from just outside the box that misses to the right of the net.
79:42 Lee Tomlin produces a right-footed shot from just outside the box that goes wide right of the goal.
77:01 Assist on the goal came from Stephen Dobbie.
77:01 GOAL - Scott Sinclair:Peterborough 1 - 3 Swansea Scott Sinclair finds the back of the net with a goal from inside the penalty box to the bottom right corner of the goal. Peterborough
75:34 Centre by Lee Tomlin, Craig Mackail-Smith conjures a right-footed shot from inside the six-yard box that clears the bar.
73:24 David Cotterill delivers the ball, Scott Sinclair produces a header from deep inside the six-yard box that clears the crossbar.
72:03 Lee Tomlin has an effort at goal from deep inside the area missing to the right of the target.
68:39 David Cotterill restarts play with the free kick.
68:39 Substitution Joe Allen on for Cedric Van der Gun.
68:39 Substitution Dave Hibbert comes on in place of Nathaniel Mendez-Laing.
68:39 Foul by Seth Nana Ofori-Twumasi on Scott Sinclair, free kick awarded.
65:07 Free kick taken by Albert Serran.
65:07 Substitution Jordi Lopez leaves the field to be replaced by Mark Gower.
65:07 Booking Darren Pratley shown a yellow card.
64:49 Booking The referee shows Lee Tomlin a yellow card for unsporting behaviour.
63:56 Free kick awarded for an unfair challenge on Darren Pratley by Lee Tomlin.
63:12 Charlie Lee produces a right-footed shot from the edge of the area and misses to the left of the goal.
62:58 Charlie Lee sends in a cross, Albert Serran manages to make a clearance.
62:34 George Boyd has an effort at goal from long distance that goes wide left.
62:10 Scott Sinclair takes a shot. Blocked by Gabriel Zakuani.
61:09 Free kick awarded for a foul by Lee Tomlin on Darren Pratley. Free kick taken by Albert Serran.
60:33 Corner taken right-footed by David Cotterill, save by Joe Lewis.
59:45 Charlie Lee takes a shot. Save made by Yves Ma-Kalambay.
59:23 Stephen Dobbie produces a right-footed shot from deep inside the six-yard box which goes wide of the left-hand upright.
58:44 Unfair challenge on Scott Sinclair by Seth Nana Ofori-Twumasi results in a free kick. David Cotterill takes the free kick.
57:47 Effort from the edge of the box by Stephen Dobbie goes wide of the left-hand post.
55:21 Substitution Chris Whelpdale goes off and Lee Tomlin comes on.
54:03 Shot on goal by Jordi Lopez from just inside the area clears the crossbar.
52:24 Nathaniel Mendez-Laing has an effort at goal from just inside the box that misses to the left of the target.
52:10 Outswinging corner taken from the left by-line by George Boyd, Darren Pratley manages to make a clearance.
50:42 A cross is delivered by George Boyd, clearance by Ashley Richards.
49:59 Scott Sinclair crosses the ball, clearance by Gabriel Zakuani.
45:56 Corner taken by George Boyd from the left by-line, Ashley Williams makes a clearance.
45:46 George Boyd takes a shot. Ashley Williams gets a block in.
45:24 David Cotterill takes a shot. Save by Joe Lewis.
45:01 The second half kicks off.
45:00+2:30 The ref blows to signal half-time.
45:00+2:06 Short corner taken by Craig Mackail-Smith.
45:00+2:00 Tommy Rowe crosses the ball, Ashley Williams manages to make a clearance.
45:00+1:01 Aaron Mclean takes a shot. Save by Yves Ma-Kalambay.
45:00+0:24 Nathaniel Mendez-Laing takes a shot. Save by Yves Ma-Kalambay.
42:07 Stephen Dobbie challenges Tommy Rowe unfairly and gives away a free kick. Free kick taken by Tommy Rowe.
40:13 Assist by David Cotterill.
40:13 GOAL - Scott Sinclair:Peterborough 1 - 2 Swansea Scott Sinclair gets on the score sheet with a goal from inside the box to the bottom right corner of the goal. Peterborough
39:13 The assistant referee flags for offside against Stephen Dobbie. Joe Lewis takes the indirect free kick.
37:36 Seth Nana Ofori-Twumasi sends in a cross, clearance made by Ashley Richards.
36:15 Corner taken by David Cotterill from the right by-line, Ashley Williams has a headed effort at goal from close range which
goes wide of the left-hand upright.
35:58 Scott Sinclair takes a shot. Save made by Joe Lewis.
33:03 Free kick awarded for a foul by George Boyd on Cedric Van der Gun. Jordi Lopez restarts play with the free kick.
30:13 Charlie Lee is penalised for handball and concedes a free kick. Darren Pratley takes the free kick.
29:10 Tommy Rowe delivers the ball.
28:44 The referee blows for offside against Stephen Dobbie. Kelvin Langmead takes the free kick.
25:37 Seth Nana Ofori-Twumasi crosses the ball, free kick awarded for a foul by Craig Mackail-Smith on Ashley Richards. Yves Ma-Kalambay
takes the direct free kick.
24:30 David Cotterill gives away a free kick for an unfair challenge on Tommy Rowe. Free kick crossed left-footed by George Boyd,
save by Yves Ma-Kalambay.
19:27 Charlie Lee takes a shot. Yves Ma-Kalambay makes a save.
19:10 Albert Serran concedes a free kick for a foul on Aaron Mclean. Nathaniel Mendez-Laing takes the direct free kick.
18:06 Free kick awarded for a foul by Alan Tate on Nathaniel Mendez-Laing. George Boyd takes the direct free kick.
17:04 Scott Sinclair sends in a cross, clearance made by Tommy Rowe.
15:02 Chris Whelpdale is penalised for handball and concedes a free kick. Alan Tate takes the free kick.
11:44 Scott Sinclair takes a shot. Clearance made by Gabriel Zakuani.
6:15 Charlie Lee provided the assist for the goal.
6:15 GOAL - Craig Mackail-Smith:Peterborough 1 - 1 Swansea Craig Mackail-Smith scores a goal from deep inside the penalty box to the bottom right corner of the goal. Peterborough 1-1
4:13 Assist on the goal came from Stephen Dobbie.
4:13 GOAL - Scott Sinclair:Peterborough 0 - 1 Swansea Scott Sinclair fires in a goal from close range low into the middle of the goal. Peterborough 0-1 Swansea.
3:04 Chris Whelpdale takes a shot. Save made by Yves Ma-Kalambay.
1:30 Inswinging corner taken by David Cotterill from the left by-line.
1:16 Scott Sinclair takes a shot. Joe Lewis makes a save.
0:00 The game gets underway.
Live text and data provided by The Press Association.
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