Burnley secured their first win at Turf Moor this season, with second half goals from Vitinho and Jay Rodriguez sealing all three points in an impressive 2-0 win.
Vitinho opened the scoring just after the hour, before Rodriguez slotted home from close range with 20 minutes left on the clock.
Vincent Kompany named an unchanged side from the team that beat Wigan Athletic 5-1 on the weekend, with just Dara Costelloe coming on the bench for CJ Egan-Riley.
First Half
The first opportunity of the game fell to the Clarets and Johann Berg Gudmundsson, as the winger cut inside and fired an effort just wide of the post from outside the area.
Millwall then had a chance of their own shortly after, as Andres Voglslammer saw his free kick excellently denied by Arijanet Muric and pushed wide for a corner.
Muric then played an integral role in the next Clarets attack, as the Kosovan shot-stopper picked out Nathan Tella, who brought the down exceptionally well, before winning a free kick just outside the box, from a Charlie Cresswell foul.
With Gudmundsson seeing his curling effort saved well by Bialkowski and away for a Burnley corner.
Kompany’s men enjoyed plenty of the ball throughout the first half, but the resolute Millwall defence stood firm to keep- the home side at bay, heading into the break goalless for the first time this season in the Championship.
Second Half
Burnley came out on the front foot in the second half, as the hosts searched for an opener, where they came close through a double effort of Rodriguez and then Tella.
Substitute Manuel Benson picked out Rodriguez in the box, who saw his low effort blocked, which bounced into the path of Tella, who forced Bialkowski into a smart save to keep the scores level.
But then just a few minutes later, the deadlock was broken on the hour, as Benson curled a terrific ball into the back post for Vitinho to head home unmarked.
And just moments later, it looked as if the Clarets had doubled their lead, as Tella latched onto a great through ball from Rodriguez and slotted home past Bialkowski, only to be flagged offside.
With 20 minutes to go, Muric was then replaced by Bailey Peacock-Farrell, after picking up a knock.
Then as the clock ticked down, the three points were all but sealed, as Rodriguez grabbed his second in as many games, turning the ball home from close range to double Burnley's lead.
The victory saw the Clarets secure their first win of the season at Turf Moor and their second clean sheet of the campaign.
Burnley: Muric (Peacock-Farrell 68), Roberts, Harwood-Bellis, Taylor, Vitinho, Cullen, Cork ©, Brownhill, Tella (Costelloe 82), Gudmundsson (Benson 56), Rodriguez (Barnes 82)
Unused Subs: Peacock-Farrell, Lowton, Bastien, Churlinov
Millwall: Bialkowski, McNamara, Wallace, Hutchinson, Cooper, Bradshaw, Cresswell, Shackleton, Fleming, Vogslammer, Saville
Unused Subs: Long, Evans, Mitchell, Malone, Honeyman, Afobe, Burey
Goals: Vitinho 62, Rodriguez 72