Burnley's stuttering start continued at London Road as a second successive defeat leaves only goal difference separating Eddie Howe's men from the early season strugglers in the bottom three of the Championship.
Two goals on his full debut from Posh frontman Emile Sinclair were enough to take the points as Keith Treacy's spectacular strike just before half-time failed to inspire a successful fightback.
The Clarets also lost goalkeeper Brian Jensen to an early groin injury which may keep the great Dane sidelined for a spell.
And while opposite number Paul Jones earned the man of the match honours, the Clarets couldn't recover from allowing Peterborough a big enough lead to cling onto to record their third home win since clinching promotion from League One.
Howe had shown a vote of confidence in the side that under-performed against Middlesbrough a week ago but didn't get the start he wanted as the Clarets went behind after just two minutes.
Peterborough hadn't previously taken the lead in a game this season or scored in the opening half hour.
Brian Jensen goes down injured
But they were straight out of the blocks and in front when Lee Tomlin lifted the ball over Burnley's static defence for Sinclair to steer an angled shot past Brian Jensen for his first Posh goal.
The pace of Sinclair was a real problem for the Clarets and only a superb goalline clearance from Ben Mee prevented the former Macclesfield Town man from making it 2-0 in a whirlwind opening from the home side.
Running onto George Boyd's through-ball, Sinclair got the better of David Edgar and beat Jensen but saw his shot cleared at full stretch by the back-tracking Mee.
Burnley could barely catch their breath or get out of their own half and from one of their innovative set-plays Peterborough went close again after 15 minutes when Ryan Tunnicliffe headed a Boyd corner just wide.
Emile Sinclair puts Posh 2-0 up
Jensen's subsequent goal-kick proved to be his last piece of action as a groin injury forced him out of the fray with Lee Grant coming on and seeing a Boyd shot whistle into the side netting before he got a meaningful touch.
But having survived the initial onslaught, the Clarets did get a foothold in the game and created a flurry of chances as they battled to get on terms.
Jay Rodriguez, without a Championship goal so far, led the charge as he headed down a Brian Easton cross for Charlie Austin to be blocked out by goalkeeper Paul Jones.
Rodriguez then hammered a shot at Jones from a Ross Wallace pass with Jones keeping out the follow-up from Chris McCann.
And Peterborough were grateful to their keeper again as he touched a David Edgar headed over the bar from Treacy's corner before Rodriguez drove an effort just wide from McCann's pull-back.
Keith Treacy finds the top corner to get Burnley back in it
But any prospect Burnley had of going into the break level disappeared after 37 minutes as they gifted Posh a second goal.
Edgar was given a difficult time by the lively Sinclair and after getting caught in possession watched in anguish as the striker weaved his way into the box before wrong-footing Grant with another assured finish.
Staring at the prospect of a long afternoon the Clarets desperately needed a lifeline and out of the blue Treacy provided it in the final minute of the first half.
The winger hadn't enjoyed the most productive of opening periods but he showed his match-changing qualities in an instant as he loaded the ball onto his right foot and hammered the ball into the top corner from 25 yards out to give the Clarets renewed hope.
Howe's men needed another goal, though, and with an hour gone the manager sent on Junior Stanislas to try and provide it.
The Clarets look for an equaliser
Still the best chances fell Peterborough's way and Sinclair should have completed his hat-trick when he was faced with just Grant to beat only to drag his shot wide after again showing the Burnley defence a clean pair of heels.
Sinclair was then thwarted again when his shot was blocked in front of goal with 20 minutes to go and with the Clarets still in the hunt, Austin was denied a possible equaliser when he ran onto a pass from Stanislas to hit an angled drive which Jones tipped over the bar.
But with the Clarets unable to build any sustained pressure, the Peterborough goal was never under serious threat again and five minutes of injury time added following prolonged treatment to Mee was not enough to prevent a second away defeat of the season for Howe's frustrated troops.
Physio Alasdair Beattie treats Ben Mee
Burnley: Jensen (Grant 17), Trippier, Mee, Edgar, Easton, Wallace (Stanislas 61), Marney (Bartley 72), McCann, Treacy, Austin, Rodriguez. Subs: Hines, Amougou.
Booked: Mee 4
Peterborough: Jones, Little, Bennett, Zakuani, Tomlin (Rowe 59), Boyd (Taylor 77), McCann, Sinclair, Tunnicliffe, Frecklington (Wootton 85), Alcock. Subs: Wootton, Kearns, Taylor, Lewis.
Booked: Wootton 87, Taylor 90
Referee: Jock Waugh
Attendance: 7,901 (1,236 Burnley)