Andre Amougou's spectacular late goal sent the Clarets into the last 16 of the Carling Cup as Eddie Howe's men came from behind to snuff out off the threat of an upset at Turf Moor.
League One high fliers MK Dons threatened to follow up their giant-killing of Norwich City in the last round when they led through an early Darren Powell goal.
But Burnley dug deep to turn the tie around with second half goals from Kieran Trippier and Amougou securing a place in Saturday's fourth-round draw.
It was never plain sailing against a Dons side looking to make history by advancing further than ever before since the club's re-formation in 2004.
But despite still searching for their best form, the Clarets showed plenty of character to dig out a morale-boosting victory sealed when the re-called Amougou netted his first goal since Boxing Day with a flying bicycle kick which was deflected past goalkeeper David Martin with just a minute to go.
Howe had made Amougou's return one of three outfield changes, including giving a full debut to summer signing Zavon Hines, in an attempt to freshen things up after back-to-back league defeats.
Andre Amougou wins it in spectacular style
But events were soon following a familiar script as the Clarets went behind after just five minutes.
What had been a bright start was punctured by the Dons' first attack as ex-Burnley loanee Luke Chadwick and Jabo Ibehre worked an opening for Powell to fire the visitors in front.
And with their fragile confidence further dented it became an uphill struggle for the Clarets to try and get back into the tie.
There was no shortage of effort with stand-in skipper Dean Marney trying to drive his troops forward.
But with nothing really coming off, it was the Dons who went closest to increasing their lead after 17 minutes when goalscorer Powell sliced wide after Chadwick and the muscular Ibehre had again caused problems.
Key to the cup door
Dean Bowditch, another former loan man back at Turf Moor, also whistled a long-range effort just wide while the Clarets tried in vain to force a real goal-scoring chance.
Jay Rodriguez battled manfully to try and add to his five goals from the first two rounds but with his goal touch deserting him he mis-cued from a Marney cross and then poked a shot wide following a Ross Wallace corner either side of an effort dragged wide from Keith Treacy.
Burnley desperately needed the lift of a goal before the break but again it was the Dons who almost snatched a second in first-half stoppage time, Powell once more the man in the right place to bring a smart save out of Lee Grant.
The Clarets responded with a positive start to the second half, Chadwick clearing off the line from a Rodriguez header, but Burnley were again grateful to Grant for keeping them in the game with another important save after 50 minutes.
Rodriguez's error allowed Ibehre to charge through and unleash a shot which Grant kept out at full stretch, Brian Easton blocking the follow-up from Powell.
And once again the value of that save was underlined nine minutes later when the Clarets finally forced a break-through to make it 1-1.
Kieran Trippier scores and celebrates his first Burnley goal
Trippier seemed an unlikely candidate to take a free-kick when Chadwick handled 25 yards from goal but the on-loan full-back showed magnificent technique to curl a right-footed effort into the bottom corner of the net to claim only the third goal of his career.
With Howe sticking to his plan to send on Charlie Austin and Chris McCann, the Clarets then pushed for the winner to avoid a third straight portion of extra-time and David Edgar went close from another Wallace corner with a shot which Sam Baldock hacked off the line.
Finally Burnley were able to take a measure of control, although Grant still had to be alert to make a flying save from substitute Anthony McNamee's deflected shot and Bowditch was only inches away from converting a Baldock cross as he rather than the ball ended up in the back of the net.
And just when it looked as though the Clarets would have to gear up for another extra 30 minutes, Amougou struck in flamboyant style, taking off to volley in Wallace's cross, with the help of a deflection off defender Tom Flanagan, to send Burnley through.
Burnley: Grant, Trippier, Edgar, Amougou, Easton, Marney (McCann 59), Bartley, Wallace, Treacy, Rodriguez, Hines (Austin 59). Subs: Stewart, MacDonald, Knowles, McCartan, Hewitt.
Booked: Easton 26
MK Dons: Martin, Chicksen, Lewington, Williams, Flanagan, Chadwick, Baldock, Potter (McNamee 59), D Powell, Ibehre, Bowditch (Collins 88). Subs: Milton, S Powell, Gyasi, Doumbe, McLoughlin.
Booked: Flanagan 3
Referee: Scott Mathieson