Paul Robinson bagged his first ever brace for Millwall as Kenny Jackett's men finally ended their awayday hoodoo in stunning style at Turf Moor.
Andros Townsend also scored for his first goal in a Lions shirt three minutes from time to send Eddie Howe's Clarets spinning to their first home defeat since he took charge on 16th January.
Not since the opening day of the season at Bristol City have The Lions hit three goals on the road - and what a way to record your first away success since 20th November!
Skipper Robbo was on target after 52 and 71 minutes, heading home Townsend's corner for the opener and then converting James Henry's delicious delivery following a short corner by the impressive Townsend.
Spurs loanee Townsend slammed home the third goal late on with a perfectly executed finish that gave Lee Grant no chance in the home goal.
Six points and two clean sheets keeps The Lions hanging on to the coat tails of the Play-Off pack and with home games against fellow promotion hopefuls Cardiff, Leeds and Swansea to come, the Championship run-in looks very interesting indeed.
"We've been talking in the week on the supporters' radio show about how long it had been since we scored from corners," said boss Kenny.
"It is something we have been practising and fortunately today Paul Robinson managed to get on the end of a couple of them.
We're still a little way away from the top six but if we can get a run of wins going, then who knows?"
Jackett made one change to his starting XI, bringing in Kevin Lisbie for Neil Harris, who sustained a hip injury in the midweek victory against QPR.
Clarets boss Eddie Howe stuck with the same side that recorded a fifth win in six games at Hull City, and was also able to name the same defensive back four for the 13th successive game.
The first half saw plenty of endeavour from both teams as Burnley, who still have an eye on automatic promotion, were frustrated by a well organised and resilient Lions rearguard.
However, it was Clarets keeper Lee Grant who was called into action first, getting a strong hand to punch clear Townsend's tantalisingly deep eighth-minute corner.
James Henry also whipped over an inviting cross crying out for a team-mate to stick out a leg and get a touch, but the ball fizzed across the face of the goal and to safety.
Burnley responded a couple of minutes later with a free-kick move clearly worked on at the training ground. Tyrone Mears chipped the ball into the mix from around 35 yards, Jay Rodgriguez peeled away from his marker and headed across to Nathan Delfouneso, whose looping header hit the top of the bar.
A sweeping move by the home side midway through the half saw Ross Wallace's neat play create an opening for the unmarked Rodriguez, and although packing a punch power-wise, Alan Dunne read the path of the ball and brilliantly blocked for a corner.
Tyrone Mears rasping, rising left foot drive flew a foot over the bar whilst at the other end Steve Morison's hooked effort from 16 yards was comfortably held under the bar by keeper Grant as The Lions tried to press forward themselves.
A quick throw from Morison saw Henry conjure up Millwall's best chance of the half on 36 minutes. The winger's sublime skill taking him past three defenders before despatching a sweet left-foot effort that curled agonisingly wide of the post.
By and large though, the opening 45 minutes was a fairly subdued affair and both sets of supporters were hoping for a bit more excitement to follow. Little, though, could the travelling Lions fans have dreamed it would turn out the way it did!
Burnley came out like a steam train after the break, but Jackett's men stopped the hosts in their tracks with 52 minutes on the clock. Townsend sent over a deep corner from the right and in ghosted skipper Robinson to head home with aplomb.
Morison so nearly conjured a second a couple of minutes later with a trademark drop of the shoulder and burst of speed down the left flank that stopped Clarets defender Danny Fox dead in his tracks. Morison's low cross was, unfortunately, just hit a tad too hard for the lurking Lisbie, who was inches from connecting.
Lions keeper Forde was called into action on 63 minutes, with a low stop to push away Ross Wallace's drive, but the big Irishman was not to be beaten for a second game in a row and produced an assured display between the sticks, ably assisted by his hard-working team-mates.
Clarets midfielder Dean Marney was lucky to escape punishment for two rash challenges in a matter of seconds, the first a raking boot that caught Liam Trotter and then an equally impetuous challenge on the impeccable Darren Ward.
Frustration had started to creep in amongst the home players and crowd as Jackett's men established a real grip on the game.
Tamika Mkandawire, Henry and Morison combined with a slick attacking move that was halted by Grant smothering Morison's shot at his near post.
Although Burnley shouted loud and long for a penalty on 66 minutes, replays showed that Robinson and Chris Iwelumo shared what could best be described as 'six of one, half a dozen of the other' in a goalmouth challenge.
A stunning break by Henry should have yielded a second goal for Millwall, but he hung on to the ball just too long and lost possession as he shaped to shoot.
However Millwall were not to be denied and when Townsend's short corner fed Henry 19 minutes from time, the precision of the finish matched that of the delivery as Robbo gleefully grabbed his - and The Lions' - second goal of the game.
On came Martin Rowlands for his first appearance in a Millwall shirt as the visitors looked to shut up shop with their two goals putting those three precious points within touching distance.
There was to be no way back for a Burnley side that simply ran up against an unbeatable Millwall back line. In fact matters went from bad to worse for the Clarets when, with just three minutes remaining, the lively Townsend was rewarded for his fine display, slamming home an angled drive from Morison's deft flick-on to wrap up victory in style.
Burnley: Grant, Fox, Duff, Carlisle, Cork, Marney (Alexander, 90mins), Eagles (Iwelumo, 60mins), Mears, Rodriguez, Wallace, Defouneso (Elliott, 67mins). Subs not used: Jensen, McCann, Bartley, Bikey.
Millwall: Forde, Dunne, Craig, Trotter, Robinson, Ward, Townsend (Barron, 87mins), Mkandawire, Lisbie (Rowlands, 78mins), Morison, Henry (Eastmond, 90mins). Subs: Mildenhall, Hackett, Marquis, McQuoid.
Scorers: Robinson (52, 70mins), Townsend (87mins)