Hat-trick of wins for Clarets
Burnley recorded their third npower Championship victory in a row as goals from Sam Vokes and Danny Ings earned them a 2-0 win at the Den.
The Clarets leapfrogged Millwall in the table and underlined their promotion credentials with a goal in each half.
Vokes opened the scoring with a neat finish following some excellent wing play from Junior Stanislas and Danny Ings made sure of the points with a close-range header.
It moves Sean Dyche's Burnley up to eighth while the Lions, now with only one win from six in the league, are down to ninth.
Danny Lafferty stole into the box early on but his attempted cross was hacked away, while Stanislas headed straight at David Forde soon after.
The visitors spurned a superb chance to take the lead when Vokes capitalised on a poor clearance from Forde, but Ross Wallace and Dean Marney got in each other's way as they looked to get on the end of Vokes' cross.
Undeterred, they pushed forward again and got their reward with 19 minutes gone.
Stanislas latched on to James Henry's misplaced pass, nutmegged Jack Smith and delivered a low cross from the byline which Vokes turned home at the near post for his third of the season.
The setback failed to stir the lacklustre Lions into life and Ings almost took advantage of more slack defending, cutting inside before firing over the bar.
It was Burnley's turn to switch off at the back next, Stanislas the culprit as he gifted possession to Henry, only for the midfielder to lift his effort clear of the bar.
Jason Shackell had to be more alert to clear Martyn Woolford's shot off the line after Kieran Trippier failed to deal with Smith's cross.
Lee Grant made a routine save from Liam Trotter's low shot and Vokes headed over from Marney's right-wing delivery as the half drew to a close.
New signing Nathan Tyson, on loan from Derby, was introduced for the second half but it was Henry who caused the problems early on.
He tricked his way past three Burnley players and crossed for Andy Keogh, but his shot on the stretch was off target.
Henry then drove in a cross which Dany N'Guessan headed wide at the far post.
But on the hour mark, and against the run of play, the away side doubled their advantage. Trippier provided the delivery and Ings the headed finish.
Having kept clean sheets in their last two league victories over Sheffield Wednesday and Crystal Palace, Burnley switched to playing on the counter-attack in a bid to make it three on the spin.
The hosts struggled to create openings despite throwing bodies forward, but they were almost undone at the other end as Trippier launched the ball downfield and Ings controlled brilliantly before clearing the bar with only Forde to beat.
Trippier cleared Trotter's goal-bound shot off the line late on to preserve Burnley's two-goal advantage and compound Millwall's frustration.