Hat-trick hero Charlie Austin and Danny Ings both enjoyed their return to the south coast as the Clarets turned on the style in the second half to push Portsmouth nearer the relegation trap door.
Former Poole Town striker Austin came off the bench to bag a stunning 20-minute hat-trick, while Ings returned to the county of his birth to claim his first goal in a Burnley shirt as Eddie Howe's men racked up a first win in eight games in spectacular style.
Ex-Bournemouth frontman Ings scored the crucial second goal just after the break to trigger a ninth away win of the season, crowned by Austin's first career treble, which had looked anything but certain at half-time.
When Kieran Trippier's early goal was cancelled out by David Norris, who has now scored home and away against the Clarets in each of the last two seasons, a familiar script looked set to unfold.
But Burnley responded superbly to prove there is still life left in their season as Howe also made it a happy 'homecoming' with the former Portmsouth defender making it two wins out of two at Fratton Park since taking over as Burnley boss.
Remarkably they have been Burnley's only two wins in 15 games against the south coast club and they did it in such style that they racked up five goals in a winning casue away from home for the first time since 1991.
Pompey's late collapse did little to help their survival hopes but, not surprising given their need for points at the bottom of the table and with successive home wins behind them, they had been quickly out of the traps.
Kieran Trippier fires the Clarets ahead
Michael Appleton's side knocked the ball around confidently but dealing with an awkward cross from Tal Ben Haim was goalkeeper Lee Grant's only early test.
That came at the cost of a corner and it was from another flag-kick shortly afterwards that Burnley turned defence into attack to grab the lead.
Ross Wallace's clearance had Pompey at full stretch with Karim Rekik just hooking the ball away from Martin Paterson at the expense of a corner at the other end.
And even though regular target Jay Rodriguez was again missing through injury, Trippier stepped into his boots to provide the lethal finish as he read David Edgar's dummy from Dean Marney's delivery to drill a sweetly stuck 20-yarder into the bottom corner.
Having been second best the Clarets couldn't have asked for more, but just three minutes later Pompey were level.
Danny Ings celebrates with Martin Paterson
The home side was causing havoc down Burnley's left side and when Luke Varney got in again his low cross was drilled into the roof of the net by Norris, who repeated the goal he scored at Turf Moor in December to give Pompey the points.
In truth the goal was no more than Pompey deserved and as they continued to take the game to the Clarets a half-time advantage looked increasingly likely.
The Burnley back four was almost constantly under pressure but did nothing to help themselves when David Edgar's poor square pass was intercepted by Allan, who raced forward and lashed a shot just over the bar.
Chris Maguire was just as elusive as Varney and the tricky Scott Allan and brought a routine save out of Grant - but that was nothing compared with the let-off Ben Haim handed the Clarets when failing to pick out a team-mate after arriving in the penalty area with a yellow shirt nowhere near him.
Ben Mee must have been longing for the sanctuary of the dressing room but a minute before the break the Clarets' left-back almost got his own back with an unlikely goal.
Charlie Austin sparks the late goal rush......
The former Manchester City man has never scored a senior goal before but after getting forward to cut inside onto his right foot, his deflected shot was sent looping towards the roof of the net before Jamie Ashdown flung himself backwards to tip the ball over the bar and send the teams in level.
And whatever Howe said at half-time evidently worked as the Clarets started the second half on the front foot and went back ahead with less than two minutes gone.
Keeping possession after Pompey had cleared a corner, Burnley worked an opening for Edgar to deliver a superb cross which Ings - pushed further forward when the Clarets adopted a midfield diamond towards the end of the first half - met with a perfectly timed run to glance the perfect header beyond Ashdown and into the far corner.
The good news didn't last long with Paterson limping off injured minutes later with a hamstring injury, but with something to hang onto the Clarets dug in and competed magnificently as the Fratton Park crowd became increasingly agitated.
.......and celebrates in style
With 20 minutes to go Pompey boss Appleton made a double change to try and launch a comeback. while the Clarets were also forced into a second substitution with Mee picking up a knock to be replaced by Josh McQuoid, with Wallace moving to left-back.
Kelvin Etuhu almost made an instant impact with a cross which Varney headed wide but it was Wallace who had more of a say with 15 minutes to go as the Clarets went 3-1 up to put the game beyond Pompey.
Wallace's excellent free-kick was missed by McQuoid but with Austin coming in behind him, the striker followed up his own touch to beat Ashdown and hook the ball in from close range.
Pompey were beginning to look a spent force and McQuoid almost got a fourth when he sent a rising drive just over the top following another forceful run from the impressive Ings.
Well played pal
The on-loan Millwall man went even closer when he brought a superb save out of Ashdown at the start of six minutes of injury time from Chris McCann's clever pass but in a fractious finish the Clarets still had time to grab two more through hat-trick hero Austin.
When Jason Pearce's woefully short back-pass allowed the striker to nip in and round the keeper, Austin helped himself to the 50th goal of his career.
And with virtually the last kick of the game Austin profited from unselfish work from McQuoid, who exploited a vacant Pompey defence to square the ball for the super-sub to complete a remarkable afternoon's work with his 14th goal of the season.
Burnley: Grant, Trippier,Mee (McQuoid 71), Edgar, Duff, McCann, Marney, Bartley, Wallace, Paterson (Austin 52), Ings (Stanislas 90). Subs: Howieson, Jensen.
Booked: Grant 60, Marney 78, Austin 90
Portsmouth: Ashdown, Ward (Etuhu 69), Rekik, Pearce, Ben Haim, Varney, Halford, Allan (Futacs 69), Norris, Thorne (Scapuzzi 82), Maguire. Subs: Rocha, Harris.
Booked: Futacs 78, Maguire 78, Norris 84
Referee: Stuart Attwell.