A stunning Ram-raid from the classy Clarets propelled them even closer to the play-offs as returning hero Chris McCann made it a day to remember at Pride Park.
Howe's that for a comeback
McCann crown a triumphant comeback from long-term injury with a fantastic fourth goal to cap a remarkable second-half comeback from Eddie Howe's rampant side.
Trailing 2-1 at the break, Chris Eagles' second goal of the game and 14th of the season got Burnley level after his penalty had been parried by Brad Jones.
Jamie Ward was dismissed for conceding the spot-kick for a foul on Tyrone Mears and against ten men the Clarets ran riot.
Elliott headed Burnley in front and with 75 minutes gone McCann applied a silky coat of gloss to a third straight win which lifts Howe's fast finishers to eighth place in the table, level on points with Nottingham Forest in the final play-off place ahead of Monday's home clash with Portsmouth.
Even before a ball was kicked it was a red letter day for McCann as the midfielder made a long-awaited return to first-team duty.
McCann started his first game since last January and only the third since he was injured a little more than a month into the Clarets' Premier League campaign in place of the unfit Dean Marney as Burnley's midfield resources were stretched.
Chris Eagles makes it 1-1
And the Irishman was forced to make a couple of morale-boosting early tackles as the Rams were quickly out of the blocks.
Robinson was a major threat and it was the on-loan Millwall man who struck after just five minutes when he turned in a low cross from Stephen Pearson.
Howe looked to counter Robinson's menace by pulling Jay Rodriguez into a wider position and after surviving a rocky opening, Burnley levelled after a quarter of an hour.
McCann was involved as he won the ball in midfield and released Wade Elliott. Elliott's deep cross was headed down by Rodriguez and then laid off by Chris Iwelumo for Eagles to calmly steer a perfectly placed shot into the corner of the net.
Lifted by the goal the Clarets enjoyed a decent spell with Rodriguez putting a half-chance wide after being played in by Elliott.
And Elliott himself then forced Brad Jones into a full-length save after he had run onto a flick-on from Iwelumo.
And then 2-2 after his penalty is saved
Derby were never prepared to lie down, though, as they looked for the result that would guarantee them Championship status and they played like a side boosted by a run of just one defeat in six games.
Robinson remained a handful and when he won a corner with just over half an hour gone, it led to Derby's second on the afternoon as they went 2-1 up.
The Clarets looked as though they had dealt with the initial threat but when the ball was only half cleared, Ward pounced to fire a deflected shot through a crowded penalty area and past Brian Jensen to give County a half-time lead.
Things almost got worse with a self-inflicted blow two minutes into the second half before Jensen came to the rescue after Pearson had been gifted a chance.
But Burnley then began to dominate as they went in search of another leveller.
McCann skidded a long-range shot just wide and Eagles and Jack Cork and Eagles then combined for Cork to see a shot deflected just wide.
From the resulting corner the old step-over routine nearly worked again as Rodriguez saw his shot headed over from in front of goal by a Rams' defender and when Danny Fox got the chance to swing over another effort, Iwelumo and Rodriguez were both close to connecting at the far post.
It was one-way traffic, though, and the pressure finally paid off with just over an hour gone when Mears, given the bird all afternoon his return to his former club, was tripped as he raced onto an Eagles' through-ball.
Ward - as he was against the Clarets in their Wembley play-off final two years ago - was sent off and even though Eagles saw his spot-kick saved by Jones, he pounced on the rebound to side-foot home and make it 2-2 and crank up the drama a further notch.
It was pulsating stuff and four minutes later the Clarets' fans were euphoric as Elliott put Burnley ahead.
Again Eagles was involved with a superb cross which Elliott, the smallest man in the box, met perfectly to head powerfully past Jones for his second goal in two games after waiting all season for a Championship goal.
Wade Elliott celebrates heading Burnley ahead
He couldn't have timed it better but even Elliott's sense of occasion had to give way to that of McCann who made the points safe 15 minutes from the end with a stunning goal.
His last goal had come on this ground on April, 2009 and after being cruelly denied almost two seasons' worth of football he announced his return in remarkable style.
Striding forward from midfield, McCann smacked a left-foot shot low from 25 yards gloriously in off the inside of a post before being replaced to a hero's reception from the Burnley fans who left with the sense of success in their nostrils.
And rightly gets mobbed
Burnley: Jensen, Mears, Fox, Duff, Bikey, Cork, McCann (Alexander 78), Elliott, Rodriguez, Iwelumo (Thompson 71), Eagles (Wallace 82). Subs: Carlisle, Delfouneso, Edgar, Grant.
Booked: Bikey 68
Derby County: Jones, Brayford, Barker, Ayala, Anderson (Addison 82), Bailey, Savage (Hendrick 80), Pearson, Ward, S Davies (Ball 77), Robinson. Subs: Doyle, Bueno, B Davies, Atkins.
Sent off: Ward 61
Referee: Mick Russell.