The Blues had been leading through Callum Lang’s first-half opener until substitute Jeremy Sarmiento levelled in the 63rd minute.
However, it looked as though John Mousinho’s men were going to hold on for an excellent point, until Josh Brownhill struck in the fourth minute of time added-on to give the hosts a 2-1 triumph.
Tough to take for the Blues, who are still searching for their first Championship win, and here are our player ratings...
1. Pompey player ratings v Burnley
The Pompey players applaud the Blues' fans at the final whistle at Turf Moor Photo: Jason Brown
2. Will Norris - 6
Such was the excellence in the centre of defence in front of him, he was given very little to save. Had no chance with wonderful finish from Sarmiento into the far corner and watched in agony as Brownhill's stoppage-time shot went past him without diving. Photo: Jason Brown
3. Zak Swanson - 7
(Replaced by Jordan Williams on 75 mins) Kept his right-back spot and, on this performance, it was a good call. Produced one superb covering interception on the stroke of half-time and always has plenty of energy to get forward. Photo: Jason Brown
4. Regan Poole - 9
Back in Pompey’s starting XI for the first time in 10-and-a-half months and how he’s been missed. Started off by producing one excellent first-half block to deny Hannibal’s shot and continued, with one remarkable block after another, crucially preventing shots on goal. Remarkable display and didn't deserve to lose. Photo: Jason Brown