The Clarets' play-off hopes were dealt a major blow as Millwall delievered a lightning strike for the second time in as many years at Turf Moor.
Millwall's 3-0 win here 12 months ago put the brakes on Burnley's last top-six challenge and the Lions all but repeated the trick to leave Eddie Howe's men as spectators in the promotion picture from 11th-place in the table.
First-half goals from Andy Keogh and Josh Wright effectively subjected the Clarets to a sixth home defeat of the season on a day when they simply failed to function.
A change of personnel and tactics did little to alter the course in the second half and Harry Kane's 70th-minute clincher confirmed back-to-back defeats for the first time since November as the Clarets - whose sole reply came via a 92nd-minute Jay Rodriguez penalty - were beaten for the third time in four games.
It was an afternoon that went wrong almost from the off for the Clarets with Millwall unlucky not to be ahead inside the opening three minutes.
Hamer Bouzza's angled drive flew past Lee Grant and crashed off the underside of the bar, cannoning down onto the line before James Henry headed the bouncing ball over the top under pressure from Ben Mee.
Lee Grant is beaten by Josh Wright's wonder goal
The Lions looked nothing like a team fighting for survival with only win Championship win to their name since Boxing Day - and missing a couple of their key players.
Kane should have made more of a break from half way as the Clarets were left wide open following a corner before Marvin Bartley got back to touch his shot wide.
But the respite was short-lived as Bartley had to clear a Paul Robinson header off the line from another Millwall corner before the visitors deservedly went ahead after a quarter of an hour.
Despite the efforts of the lion-hearted Michael Duff, the Clarets were all at sea at the back and it was a combination of errors that allowed Keogh to opening the scoring.
David Edgar's mistake could not be rescued by Mee, who could only help the ball into the path of the Millwall striker who calmly made space to hammer a left-foot shot into the roof of the net.
Ross Wallace tries to get the Clarets back in it
Missing the patrolling presence of Dean Marney in midfield following the birth of his first child over night, Burnley were frequently left stretched in an incredibly open game.
Chris McCann did his best to force Millwall back and he was behind the Clarets' best moments of the opening half.
But Rodriguez and then Kieran Trippier were unable to convert chances created by the Burnley skipper and with half an hour gone the Clarets found themselves 2-0 down to one of the best goals scored at Turf Moor in a long time.
Harry Kane makes it 3-0 and game over
Wright had never scored in a handful of games for the Lions and the midfield man is unlikely to hit a finer strike as he thumped home a first-time volley from 30 yards after a headed clearance from Mee had dropped invitingly into his path.
Ten minutes later the Clarets then lost McCann to an injury which left their midfield department even more bereft and forced a rapid re-shuffle from Howe, as Martin Paterson came on to be followed by Danny Ings and Brian Easton during the break as the Burnley boss tried to mastermind a fightback.
With a switch to three at the back and Easton and Kieran Trippier employed as wing-backs the Clarets tried to force the issue.
Jay Rodriguez scores his 19th of the season from the spot
But they needed the tonic of an early goal to put some pressure on the visitors and in truth it didn't look like coming with a couple of Ross Wallace efforts and a deflected attempt from Ings the closest the Clarets came.
Wallace curled another shot just wide but Millwall were happy to sit back and soak up what pressure came their way before making sure of the points with 20 minutes to go.
Kane timed his run perfectly to collect Henry's through-ball and from an on-side position raced through to slip the ball past Grant and put Burnley out of their misery, Rodriguez's injury-time penalty for a trip on Bartley by Shane Lowrynot even scant consolation.
Burnley: Grant, Trippier, Mee, Duff, Edgar, McCann (Paterson 39), Bartley, Wallace, Rodriguez, Austin (Ings ht), Treacy (Easton ht). Subs: Hines, Jensen.
Millwall: Forde, Dunne, Craig, Robinson, Bouazza (Feeney 83), Henry, Keogh, Abdou,Lowry, Kane (Henderson 88), Wright (Barron 75). Subs: N'Guessan, Allsop.
Referee: David Phillips.
Plenty to think about for Eddie Howe