The Clarets' wait for a first away win of the season was extended beyond eight games as the three points needed even more urgently by Portsmouth went the way of the bottom club thanks to second-half goals from Hermann Hreidarsson and Aruna Dindane.
Dindane had earlier missed a penalty as Burnley goalkeeper Brian Jensen threatened to pile further misery on the troubled home side, whose players received their overdue wages just the night before the game.
But with the Clarets lacking the finishing power to make the most of their reprieve, Pompey earned themselves a win bonus for only the third time this season to revive their survival hopes.
Hreidarsson, who went tamely to ground to 'earn' the harshly given penalty, broke the deadlock in the 64th-minute and six minutes from the end Dindane made amends for his miss by heading in the second goal.
Burnley were left to rue wasted opportunities of their own as they failed to score for the first time in seven games but, just as crucially, showed again how elusive clean sheets are proving in their quest to keep the Barclays Premier League strugglers at arm's length.
For the first time in six games Burnley boss Owen Coyle was forced to change his starting line-up with Steven Caldwell's one-match suspension earning Kevin McDonald a full Premier League debut.
McDonald's selection in central midfield, with Andre Bikey resuming defensive duties, also led to a tactical switch as Wade Elliott moved out to the right wing with Robbie Blake offering central support for top scorer Steven Fletcher.
And it was Elliott who was instrumental in Burnley's best two opportunities of a cagey opening half-hour.
The first came as Blake launched a swift counter-attack from inside his own half with an early ball out to Elliott whose run and cross saw Fletcher give Pompey defender Marc Wilson the slip.
Having made room for the shot and with just Asmir Begovic to beat the Scot must have fancied his chances of adding to his eight-goal tally but with his weaker right foot he failed to make decent contact and didn't even force the keeper to save.
The right flank was proving a productive area for Burnley, though, and when they worked another opening Elliott got behind the Pompey defence but could not pick out Fletcher or Chris Eagles.
It was a case of nearly but not quite as a number of promising Burnley moves, with McDonald, Eagles and Blake also prominent, broke down on the edge of the Portsmouth penalty area and with 32 minutes gone the struggling home side was gifted the chance to go in front.
Referee Phil Dowd was duped into awarding a poor penalty decision when Hreidarsson went down under a non-existent challenge from Elliott but erratic striker Dindane failed to capitalise as his weak spot-kick was well saved by Jensen.
That summed up a pretty miserable first half for Portsmouth's leading scorer who earlier failed to control a pass from the dangerous Kevin-Prince Boateng when a decent touch would have left him with just Jensen to beat from in front of goal.
However, the penalty miss did appear to fire up Pompey and Dindane almost made amends when he robbed Bikey - who thought he should have had a penalty at the other end when Hreidarsson grabbed him by the collar - but failed to pick out a team-mate as Jensen again came to the Clarets' rescue.
With both the home side and the home crowd visibly and audibly edgy the incentive for Burnley to get the first goal was massive and seven minutes into the second half they almost found it.
A poor pass from Tal Ben Haim allowed Eagles the chance to run at the defence and even though the initial move broke down, Burnley kept possession for Fletcher to tee up McDonald for a thumping 25-yard drive which Begovic tipped over the bar at full stretch.
The Clarets were getting closer and moments later McDonald picked out Fletcher who worked the ball onto his left foot and fired a low shot just beyond the far post.
Fletcher looked the most likely source of a goal and only a stunning save from Begovic prevented him from swinging a magnificent long-range volley into the top corner.
But with Pompey desperate for a win to aid their survival hopes, Avram Grant had thrown on Kanu and the talismanic striker made an immediate impact with a decisive contribution to Hreidarsson's crucial opening goal.
Kanu's perfect lay-off from a Boateng pass left Hreidarsson in the clear and the veteran Icelander made no mistake with a left-foot strike across Jensen and into the far corner.
If Boateng had been as clinical with an equally good chance from another fine Kanu pass seven minutes later Burnley would have been left facing a virtually impossible task but with Coyle sending on Steven Thompson and Fernando Guerrero they harboured hopes of a late leveller.
Bikey headed another corner over the top but the earlier chances had begun to dry up and when Dindane nodded in a cross from O'Hara the Clarets were left to look ahead to back-to-back home games against Fulham and Arsenal to get their campaign back on track.
Burnley: Jensen, Alexander, Carlisle, McDonald, Fletcher, Elliott, Mears, Blake (Thompson 68), Bikey, Jordan, Eagles (Guerrero 73). Subs: Penny, Kalvenes, Duff, Gudjonsson, Easton.
Portsmouth: Begovic, O'Hara, Hreidarsson, Brown, Finnan, Smith (Kanu 59), Boateng (Mullins 90), Dindane, Ben Haim, Yebda, Wilson. Subs: Piquionne, Vanden Borre, Hughes, Belhadj, Ashdown.
Referee: Phil Dowd