Clarets skipper Clarke Carlisle may well be the brainiest professional in the game, but he showed a distinct lack of ability in his defending as poor challenges conceded two second-half penalties.
Any doubts that Portsmouth's financial plight would affect their performance were quickly dispelled and the visitors were unlucky not to take an early lead when from a short corner striker Danny Webber glanced the ball into the net, but was unfortunate to see his effort ruled out for offside.
Webber then turn provider for the opening goal as his cross come shot was turned in at the far post by Frederic Piquionne.
Burnley's response came as strikers Robbie Blake and Steven Fletcher linked up, but the Scotland forward blazed over the crossbar.
The home side equalised when a long ball downfield from goalkeeper Brian Jensen was flicked on by Fletcher for Martin Paterson to coolly lob the ball over the stranded David James.
Portsmouth substitute John Utaka created an opportunity with his first touch, but midfielder Jamie O'Hara was unfortunate to see his effort strike the crossbar.
Portsmouth should have gone in front when they were awarded a penalty by referee Mark Clattenburg as Carlisle needlessly brought down Piquionne, but O'Hara's spot-kick was beaten away by Jensen diving to his left.
Burnley should have taken advantage of that reprieve as Paterson got to the byline down the right and crossed to the edge of the six-yard box, but Fletcher put his header over the crossbar.
Pompey were then awarded a second penalty as Carlisle hesitated after receiving a throw-in inside the penalty area and was penalised for bringing down Utaka.
This time the spot-kick was taken by Hassan Yebda and he made no mistake by calmly placing his left-foot effort inside Jensen's left-hand upright.
Portsmouth had to play the last few minutes with ten men after defender Ricardo Rocha received a second yellow card, but the visitors held firm to deservedly collect the three points.