Ashley Barnes' second goal in successive games was cancelled out by a late Tom Bradshaw equaliser at the Den on Tuesday night as the Clarets drew 1-1.
The striker, who bagged the winner at Luton on Saturday, fired in the Clarets' goal in the 52nd minute before Bradshaw struck with five minutes to play to ensure the points were shared in South Bermondsey.
Manager Vincent Kompany made four changes from the side that beat Luton Town on the weekend.
The Clarets’ attack was altered as Anass Zaroury and Vitinho came in for Johann Berg Gudmundsson and Nathan Tella.
Meanwhile Ameen Al-Dakhil and Scott Twine were handed their first starts in the league replacing Charlie Taylor and Jack Cork respectively.
First Half
The Clarets dominated the opening 10 minutes in London and came close to an early opener when Barnes raced forward in attack before picking out Zaroury to his left, but the Moroccan’s effort was tipped wide for a corner by the hand of Long.
Shortly after, Barnes had a chance of his own when Vitinho fired a low cross into the box only for the striker to steer the ball narrowly wide of the post.
Kompany’s men then carved open another break as Zaroury beat McNamara down the left before lifting a dangerous ball into the area which reached Cullen, but the centra midfielder saw his ball back into the box cleared away by the head of Cooper.
The visitors were in cruise control and had another shot towards goal just two minutes later when Zaroury intercepted a defensive error and teed up Twine on the edge of the area to fire just inches wide of the goal.
As half time approached Millwall applied pressure on the Burnley defence and had their first real opportunity on goal when Flemming intercepted Ekdal’s pass and rifled an effort from outside the box into the hands of Muric.
Second Half
It took the Clarets just seven minutes into the second half to break the deadlock and it was a well worked move from Kompany’s men to open the scoring.
Twine fed the ball out wide into the path of Zaroury who played it back to Twine on the edge of the six-yard box to fire at goal, but a block from Creswell fell to Barnes who made no mistake of hammering it home past Long from close range.
The woodwork then denied Burnley a second goal on the hour mark when Brownhill saw his strike bounce off the right side of the post.
Maatsen then got in on the action and went for goal from 25-yards out forcing Long to push it wide for a corner.
The hosts made a triple change with 20 minutes to go in search of an equaliser and it was substitute Bradshaw who fired in from a corner late on.
Burnley: Muric, Roberts, Al-Dakhil, Ekdal, Maatsen (Taylor 83), Brownhill, Cullen, Zaroury (Cork 83), Vitinho (Tella 87), Twine (Gudmundsson 72), Barnes
Unused Subs: Peacock-Farrell, Obafemi, Foster
Millwall: Long, McNamara, Wallace, Cooper, Flemming, Cresswell, Shackleton (Leonard 72), Watmore (Esse 72), Voglslammer, Saville (Bradshaw 72), Honeyman
Unused Subs: Bialkowski, Evans, Malone, Emakhu
Goals: Barnes 52’, Bradshaw 85’