David Norris struck in injury time of a scrappy encounter to give Portsmouth a first away win since March and end Burnley's three-game winning streak.
The former Ipswich man smashed a left-footed shot into the bottom corner with virtually the last kick of the game.
Pompey's Luke Varney missed from close range in the third minute, while Ross Wallace saw two long-range efforts go wide for Burnley in the second half.
Chris McCann also headed wide for the hosts before Norris's late strike.
The midfielder clearly has a knack of scoring against the Clarets, having netted home and away against them for Ipswich last season, though he had passed up a presentable earlier chance, prodding Greg Halford's cross wide with 12 minutes left.
His last-gasp strike might not have been needed had Varney managed to convert a close-range opportunity for the visitors in the opening exchanges, after Clarets' goalkeeper Lee Grant parried Norris's shot into his path.
However, the former Charlton man was unable to make a clean contact and Kieran Tripper cleared.
After quarter of an hour, Varney lobbed the ball towards goal before colliding with Grant, leading to penalty appeals from the visitors but referee Steve Rushton signalled a home free-kick.
Two periods of treatment followed for Varney, who was eventually substituted for Erik Huseklepp.
Burnley looked low on confidence for a team on a run of three straight victories and it was the second half before Wallace drilled a free-kick narrowly wide.
The visitors responded with a sweeping move that resulted in Huseklepp angling a volley narrowly past the post from inside the area.
Norris's late intervention sealed back-to-back victories for new Pompey boss Michael Appleton, and lifted them to 16th in the Championship, a place and a point behind their opponents.
Burnley manager Eddie Howe: "I thought we had got over the late goal drama against us. We have had it already this season against Reading and Leeds and it is another lesson we have to learn.
"I didn't see the goal coming because I thought we were on top in the half. It was a slow and scrappy game but you have to give credit to Portsmouth because they defended well and nullified our attacking threat.
"It looked like we were heading for a 0-0 and we would have taken that even though it wasn't the result we were looking for.
"There is only anxiety when we don't play well. The atmosphere does get across to the players and it was quite quiet. That isn't a criticism of the fans because they want to be entertained and we did not do that."
Portsmouth manager Michael Appleton: "The away record is something that has been spoken about before but I never mentioned it all week.
"I said to them just two minutes before they went out that there is no difference - the pitch is the same size, the grass is green and you play against 11 men. The only difference is that you get cheered at home and booed away. To get the win was great for us.
"Going into injury time you don't want to lose the game and getting the clean sheet was my main focus.
"We are just trying to stay focused on what happens on the pitch rather than off it. I said the other week, and I was half serious, that it helps having a couple of players who aren't the brightest because they can't think about it."