BURNLEY face a tough task if they are to stretch a five-game unbeaten run and stay in the play-off hunt.
The Clarets came under pressure from Millwall from the start, with Hamer Bouazza firing a shot off the underside of the crossbar in the third minute. Neither Andy Keogh or James Henry could convert their follow-up headers.
The let-off didn't last long, though, as Keogh capitalised on a David Edgar error and fired past Lee Grant in the 15th minute.
Josh Wright doubled Millwall's lead with an unstoppable dipping 30-yard volley.
Burnley were forced into a change six minutes before the break when Chris McCann went off with what looked like a hamstring problem.
With Josh McQuoid ineligible for selection against his parent club and Dean Marney unavailable after his wife gave birth to their first child overnight, the captain was replaced by Martin Paterson.