The Clarets launched their FA Cup campaign in highly efficient style as first-half goals from Graham Alexander and Steven Fletcher snuffed out any prospect of a shock exit at stadiummk.
Burnley's away record of nine defeats in ten games in the Barclays Premier League might have had MK Dons dreaming of possible glory and a place in round four.
But despite a brave fightback and an 89th-minute goal from substitute Dean Morgan, the League One side was rarely given a sniff of a chance as the Clarets secured a first victory in ten games to give manager Owen Coyle a 50th win as Burnley boss.
Alexander swiftly banished any nerves with his fifth successful penalty of the season mid-way through the first period.
And top scorer Fletcher then added his ninth goal of the campaign after 35 minutes with a classy finish which emphasised the gulf between the two sides as Burnley went into the hat for the last 32.
Wade Elliott and Fletcher both hit the woodwork after the break and with goalkeeper Brian Jensen standing firm until the 89th-minute, the Clarets started 2010 in perfect style with a confidence-building first away win since August.
With speculation swirling around concerning the future of Coyle following reported interest from Bolton, frozen conditions up north and a tricky playing surface, this might have had the ingredients of an upset and the Clarets certainly started in uncertain fashion.
Fletcher is fouled to give Burnley their spot-kick
Suspensions for Tyrone Mears and Stephen Jordan and David Nugent's ineligibility meant three changes to Burnley's starting line-up with Richard Eckersley, Christian Kalvenes and Robbie Blake all coming in.
And after a nervy opening quarter-of-an-hour, in which the Dons launched a couple of unthreatening long-range efforts, it was Blake who got Burnley moving.
The forward had barely had a kick until Coyle sent him out to the left flank in a return to the 4-5-1 formation which the Clarets have used for much of the season.
And Blake immediately made his mark by cutting in to fire a low shot just past the post.
Blake and Steven Fletcher suddenly looked a dangerous combination, although it was all Fletcher's work which brought the Clarets the opening goal.
Robbing Dons' skipper Dean Lewington, Fletcher then went past Mathias Doumbe and went down over the defender's outstretched leg to allow Alexander to drill home his sixth goal of the season from the penalty spot.
The goal helped settle the Clarets with Chris Eagles continuing his impressive recent form and looking a threat each time he went forward, although Brian Jensen had to be alert to dash off his line at the other end to reach Danny Woodards' fine through-ball ahead of top scorer Jermaine Easter.
Alexander does the business from the spot
But Burnley continued to carry the greater menace and doubled their lead ten minutes before the break to give themselves some welcome breathing space.
The Clarets had just gone close through Blake, whose goalbound effort was blocked by Woodards, when more magic from Eagles gave Fletcher the chance to make it 2-0.
Well spotted by Eagles, Fletcher collected his perfectly weighted pass 22 yards from goal, worked the ball onto his left foot and then steered a low shot past Willy Gueret into the bottom corner from the centre of the goal.
That looked to have ensured a safe passage through, although the Dons issued a reminder that they would not give up their dream without a fight in first-half stoppage time when a Woodards header was saved by Jensen and scrambled off the line before Doumbe saw his follow-up effort blocked by Ecklersley.
A third goal would have removed all doubt and five minutes into the second half the Clarets were only the width of the crossbar from providing it.
When Fletcher was fouled Blake lined up a free-kick and although his effort hit the wall, the ball dropped kindly for Elliott, who poked a shot against the woodwork at full stretch.
Typically, the Clarets refused to shut up shop as Dons' boss Paul Ince sent on ex-Burnley loanee Luke Chadwick to try and engineer a way back into the tie for the underdogs.
But again it was Burnley who went close when Eagles crossed from the right and Fletcher saw a header clip the outside of a post.
Fletcher steers home his ninth goal of the season to secure victory
As well as wins, clean sheets have also been in short supply for the Clarets in recent weeks but Jensen did his best to secure a shut-out with two fine saves to repel the Dons' as Ince's men wound up for a defiant late push.
First Jensen got down low to keep out Peter Leven's low shot and the big keeper then stood firm to block with his face as Chadwick ran through onto another fine pass from the impressive Jason Puncheon.
A goal then would made it a nervy finish for the Clarets and only a timely block from Michael Duff prevented substitute Jude Stirling from pulling one back with ten minutes to go.
The Dons did finally get their reward when Morgan fired into the roof but by then the clock was against them and while there were some heart-stopping moments in injury time when the ball bounced around the Clarets' box, Coyle's men had done enough to ease through.
Burnley: Jensen, Alexander, Kalvenes, Duff, McDonald (Gudjonsson 71), Fletcher (Thompson 88), Elliott, Eckersley, Blake, Bikey, Eagles. Subs: Penny, Edgar, Easton, Guerrero, Harvey.
MK Dons: Gueret, Lewington, Doumbe, Gleeson, Easter (Morgan 80) , Wilbraham, Baldock (Chadwick 55), Woodards, Puncheon, Howell (Stirling 80), Leven. Subs: Johnson, Carrington, Gobern, Powell.
Referee: T Bates