A goal from Noel Whelan preserved Dennis Wise's undefeated record as a manager but Millwall really should have had all three points against a Burnley side that had conceded eight goals in its previous two matches.
Millwall were in the box seat when Whelan, on as a substitute got round the back of the Burnley defence to head home at the second attempt, after Robbie Ryan's cross had been flicked on by Bob Peeters.
The only surprise was that it took the Lions 53 minutes to turn their territorial advantage into a tangible return.
During a one-sided first half they had the Clarets on the ropes more than once and giant striker Peeters was twice denied by the agility of Burnley keeper Brian Jensen.
Even the loss of striker Neil Harris to injury after just 27 minutes didn't effect Millwall and Jensen had to make another fine save to deny Paul Ifill.
However, Millwall paid the price for sitting back after going ahead and an equaliser from Ian Moore, who scored with a clever flick at the post on the hour, gave Burnley heart.
The Clarets' Delroy Facey was denied by Tony Warner from point-blank range in the closing stages, but the best late chance fell to the visitors with substitute Kevin Braniff hitting the foot of a post.