Pompey on Friday became the first top-flight club to enter into administration, but the players rolled up their sleeves to add to Burnley's own relegation fears.
Although Martin Paterson equalised Frederic Piquionne's opener in the first half, Hassan Yebda grabbed the winner from the spot 15 minutes from time for the visitors who ended the game with 10 men when Ricardo Rocha was dismissed late on.
At present Portsmouth stand five points from safety, but that will become 14 when the Premier League board ratify a nine-point deduction that comes with administration.
With only 33 to play for, Avram Grant's side are staring relegation in the face, and the Clarets will likely join them on the basis of this display.
Portsmouth were undoubtedly the more forthright side during the opening exchanges, and deserved their lead when it came in the 25th minute.
Prior to that the industrious Danny Webber had dragged one effort wide when well placed after Leon Cort had inadvertently steered an attempted through-ball from Quincy Owusu-Abeyie into the striker's path.
Pompey had the ball in the back of the net soon after but celebrations were caught in the throats of their faithful followers as Webber was marginally offside in steering home at the near post a left-wing cross from Nadir Belhadj.
Any thoughts it was going to be another of those afternoons at that stage were then swiftly dispelled when Piquionne made it two goals in successive games.
Webber again played his part, albeit dragging another shot that was heading two yards wide until on-loan Lyon forward Piquionne steered the ball home at the far post, prompting an optimistic chorus of "We are staying up."
However, Portsmouth would not be bottom of the table but for their defensive fragility, and it duly reared its head in the 31st minute, their lead lasting just six minutes.
From Brian Jensen's long goal-kick, Steven Fletcher appeared to faintly flick the ball on into the area where an awaiting Paterson superbly lifted it over David James who was rooted to his six-yard line.
Anybody expecting Portsmouth to crumble after that were again sorely mistaken as they could have headed into the interval having restored their lead.
The unfortunate O'Hara, however, was denied by the left-hand post after delightfully beating Jensen from 20 yards with a left-foot curler delivered with his instep.
Pouncing on the rebound, Webber cracked a half-volley goalwards, but was thwarted by the bravery of Danny Fox who threw his body in the way to block.
O'Hara then wasted a golden opportunity to restore his side's lead in the 55th minute when Clarets captain Clarke Carlisle was made to look none too clever.
Carlisle appeared on Channel 4's Countdown in midweek, winning two games, which light-heartedly led to his name on the team sheet being jumbled up, akin to the conundrum part of the programme.
But Carlisle's challenge just inside the area and with Piquionne running away from goal was a needless one, leaving Mark Clattenburg with an easy decision.
On-loan Spurs midfielder O'Hara then took on the responsibility, and although his left-foot spot-kick was firm enough, Jensen was the hero by diving the right way and blocking with his body.
It was a let-off Burnley should have punished five minutes later with a breakaway move down the right wing involving Elliott and Paterson.
Paterson's delivery into the heart of the area was a piercing one, picking out an unmarked Fletcher who was left with his head in his hands after heading over from five yards.
Fletcher's embarrassment, however, was nothing to that of Carlisle who gave away a second penalty in the 75th minute, tugging on the shirt of substitute John Utaka after he had lost the ball inside his own area, earning himself a booking in the process.
This time it was another of Pompey's on-loan players in Benfica midfielder Yebda who stepped up, sending Jensen the wrong way for only his second goal for the club, and first since October 3.
The home side naturally dominated the closing stages as they went in search of a second equaliser, a task made easier in the first of four minutes of injury time when Rocha was sent for two bookable offences.
But despite bombarding the Pompey area, James was never troubled, leaving Burnley with a miserable record that has now seen them win just one of their last 16 league matches.