Josh Wright's long-range volley helped Millwall secure their first win in six league games to move the Lions seven points clear of the relegation zone.
Andy Keogh capitalised on David Edgar's error to open the scoring before Wright hit an unstoppable 30-yard volley.
On 70 minutes James Henry found Harry Kane, who fired past the advancing Burnley goalkeeper Lee Grant.
Jay Rodriguez pulled a goal back with an injury-time penalty after Shane Lowry fouled Marvin Bartley.
Millwall's ambitious approach was signalled early on when Hamer Bouazza's effort cannoned against the underside of the bar, while Kane was denied by a last-ditch interception from Bartley, who then cleared Paul Robinson's header off the goal-line.
Edgar proved less diligent in defence and when he botched a routine clearance and Keogh was on hand to provide a left-footed finish.
Millwall went 2-0 up when Henry's left-wing free-kick was headed clear by Ben Mee and the ball looped up for Wright to thrash home.
Burnley captain Chris McCann then hobbled out of the action to be replaced by Martin Paterson, with Burnley boss Eddie Howe also introducing two more substitutes - striker Danny Ings and defender Brian Easton - at the interval in a bold attempt to get back into the game.
If those substitutes produced a more significant Burnley threat, the game slipped further out of their grasp when Henry set up Kane for the third goal.
Burnley's goal came in stoppage when Rodriguez's penalty gave him his 19th goal of the season, with the defeat leaving Howe's side six points shy of the play-off places.
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Live Text Commentary
Full Time The final whistle is blown by the referee.90:00 +2:43 Goal scored
Goal! - Jay Rodriguez - Burnley 1 - 3 Millwall Power penalty scored by Jay Rodriguez. Burnley 1-3 Millwall.90:00 +1:33
Marvin Bartley fouled by Shane Lowry, the ref awards a Penalty.90:00 +0:45
Unfair challenge on Ross Wallace by James Henry results in a free kick. Free kick crossed by Ben Mee.90:00 +0:01
Ross Wallace takes a shot. Save by David Forde. Ben Mee fouled by Darius Henderson, the ref awards a free kick. Direct free kick taken by Lee Grant.89:39
Tony Craig gives away a free kick for an unfair challenge on Kieran Trippier. Direct free kick taken by Kieran Trippier.89:08
James Henry concedes a free kick for a foul on David Edgar. Direct free kick taken by Ben Mee.88:03
The assistant referee flags for offside against Jay Rodriguez. David Forde takes the indirect free kick.87:17 Substitution
Substitution Darius Henderson replaces Harry Kane.86:52
Liam Feeney handles the ball and concedes a free kick. Michael Duff takes the direct free kick.85:32
Free kick awarded for a foul by David Edgar on Andrew Keogh. Free kick taken by Alan Dunne.85:08
The referee gives a free kick against James Henry for handball. Free kick taken by Ben Mee.83:00
Harry Kane takes a shot. Michael Duff gets a block in. Outswinging corner taken right-footed by James Henry played to the near post, clearance made by Jay Rodriguez. Outswinging corner taken right-footed by James Henry, Michael Duff makes a clearance.81:21
Ross Wallace takes the outswinging corner, Alan Dunne makes a clearance.81:21 Substitution
Substitution Hamer Bouazza goes off and Liam Feeney comes on.78:32
The referee blows for offside. Indirect free kick taken by David Forde.75:37
The assistant referee flags for offside against Martin Paterson. Free kick taken by Alan Dunne.74:40
Handball decision goes against Ross Wallace. Alan Dunne restarts play with the free kick.73:48 Substitution
Substitution (Millwall) makes a substitution, with Scott Barron coming on for Josh Wright.73:38
Brian Easton has an effort at goal from just outside the box which goes wide of the left-hand post.
Effort from outside the area by Ben Mee goes wide right of the goal.70:59
Free kick awarded for an unfair challenge on Danny Ings by Josh Wright. Direct strike on goal from the free kick comes in from Ross Wallace, blocked by Tony Craig.70:36
Ross Wallace fouled by Josh Wright, the ref awards a free kick. Ross Wallace takes the direct free kick.69:13
James Henry provided the assist for the goal.69:13 Goal scored
Goal! - Harry Kane - Burnley 0 - 3 Millwall Harry Kane scores a goal from deep inside the penalty area to the bottom right corner of the goal. Burnley 0-3 Millwall.67:30
James Henry is penalised for a handball. Ross Wallace restarts play with the free kick.66:40
The referee penalises Nadjim Abdou for handball. Ben Mee takes the indirect free kick.66:10
Foul by Ross Wallace on Nadjim Abdou, free kick awarded. Alan Dunne takes the direct free kick.65:39
Andrew Keogh gives away a free kick for an unfair challenge on Michael Duff. Ben Mee takes the direct free kick.65:06
Ross Wallace has an effort at goal from just outside the area which goes wide of the left-hand post.64:04
Corner taken right-footed by Ross Wallace, save made by David Forde.63:37
Danny Ings takes a shot. Josh Wright gets a block in.63:05
Corner taken left-footed by Kieran Trippier, save by David Forde.61:36
Outswinging corner taken from the right by-line by Kieran Trippier, clearance made by Tony Craig.60:54
Danny Ings has an effort at goal from just outside the box which goes wide of the left-hand post.60:05
Ross Wallace takes the outswinging corner, Brian Easton takes a shot.59:51
Ross Wallace takes a shot. Andrew Keogh gets a block in.57:01
The ball is crossed by Brian Easton, save made by David Forde.55:57
Effort from just outside the box by Hamer Bouazza goes over the bar.53:59
Ben Mee concedes a free kick for a foul on James Henry. David Forde takes the free kick.53:15
Ross Wallace takes a shot. Blocked by Tony Craig.52:49
Corner taken by Kieran Trippier from the right by-line played to the near post, clearance by Andrew Keogh.51:15
Jay Rodriguez fouled by Hamer Bouazza, the ref awards a free kick. The free kick is swung in right-footed by Ross Wallace, save made by David Forde.49:28
Kieran Trippier fouled by Andrew Keogh, the ref awards a free kick. Lee Grant takes the free kick.48:45
Inswinging corner taken left-footed by Hamer Bouazza from the right by-line, Danny Ings makes a clearance.47:40
Jay Rodriguez takes a shot. Blocked by Alan Dunne.47:13
Alan Dunne fouled by Martin Paterson, the ref awards a free kick. James Henry takes the direct free kick.46:07
The assistant referee signals for offside against Hamer Bouazza. Lee Grant takes the indirect free kick. Free kick awarded for an unfair challenge on Martin Paterson by Alan Dunne. Free kick taken by Ross Wallace.45:01
The second half begins.45:01 Substitution
Substitution Danny Ings comes on in place of Charlie Austin.45:01 Substitution
Substitution Brian Easton replaces Keith Treacy.45:00 +3:07 Half time
Half Time The ref blows to end the first period.45:00 +1:36
Ross Wallace has an effort at goal from close in which goes wide right of the goal.45:00 +0:09
Inswinging corner taken right-footed by Kieran Trippier, Michael Duff takes a shot. Save by David Forde.38:18 Substitution
Substitution Martin Paterson replaces Chris McCann.37:09
The assistant referee signals for offside against Charlie Austin. Free kick taken by David Forde.33:23
Inswinging corner taken by Ross Wallace from the right by-line.31:53
Harry Kane is flagged offside by the assistant referee. Free kick taken by Lee Grant.30:22
Corner taken left-footed by Ross Wallace from the right by-line, David Forde makes a clearance.29:08 Goal scored
Goal! - Josh Wright - Burnley 0 - 2 Millwall Josh Wright finds the back of the net with a goal from outside the penalty box high into the middle of the goal. Burnley 0-2 Millwall.28:39
Unfair challenge on Hamer Bouazza by Jay Rodriguez results in a free kick. Free kick crossed by James Henry, Ben Mee manages to make a clearance.25:26
Ross Wallace takes a shot. Blocked by Alan Dunne.22:34
Andrew Keogh gives away a free kick for an unfair challenge on Michael Duff. Direct free kick taken by Lee Grant.21:56
Foul by Jay Rodriguez on Josh Wright, free kick awarded. David Forde takes the direct free kick.21:14
Josh Wright gives away a free kick for an unfair challenge on Jay Rodriguez. Direct free kick taken by Ben Mee.20:03
Chris McCann produces a left-footed shot from just outside the penalty area that goes harmlessly over the target.19:11
Unfair challenge on Kieran Trippier by Tony Craig results in a free kick. The free kick is swung in right-footed by Ross Wallace, clearance made by Andrew Keogh.18:32
Corner from the right by-line taken by Kieran Trippier, Harry Kane manages to make a clearance.16:54
Charlie Austin is flagged offside by the assistant referee. Indirect free kick taken by Shane Lowry.16:27
Marvin Bartley concedes a free kick for a foul on Harry Kane. Free kick taken by Alan Dunne.14:28 Goal scored
Goal! - Andrew Keogh - Burnley 0 - 1 Millwall Andrew Keogh scores a goal from deep inside the penalty box to the bottom left corner of the goal. Burnley 0-1 Millwall.14:04
The ball is crossed by Chris McCann, Tony Craig gets a block in.13:08
Harry Kane produces a right-footed shot from just outside the area that goes harmlessly over the bar.11:54
Inswinging corner taken by Hamer Bouazza, Paul Robinson takes a shot. Marvin Bartley makes a clearance.11:25
Corner from the left by-line taken by James Henry, Lee Grant makes a save.10:19
Ross Wallace takes a short corner. Ross Wallace takes a shot. Tony Craig gets a block in.7:56
Keith Treacy produces a left-footed shot from just outside the box that misses to the right of the goal.5:27
Free kick awarded for a foul by Shane Lowry on Jay Rodriguez. Kieran Trippier crosses the ball from the free kick left-footed from right channel, clearance made by Tony Craig. Inswinging corner taken by Ross Wallace from the left by-line.4:34
James Henry takes a shot. Blocked by Kieran Trippier. James Henry takes a inswinging corner from the left by-line to the near post, David Edgar makes a clearance.4:01
Keith Treacy is penalised for a handball. The free kick is swung in left-footed by Hamer Bouazza, clearance by David Edgar.2:25
Hamer Bouazza takes a shot. James Henry produces a header from deep inside the six-yard box that clears the crossbar.0:00
The ref blows the whistle to start the match.
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