Richard Sadlier's goal six minutes from time gave Millwall a deserved point against the Clarets.
Ian Moore's third goal in four games had given the Clarets an 18th minute lead at the New Den.
But the home side piled forward throughout the second half and sub Sadlier denied Burnley a fourth straight league win and dented their play-off hopes. He almost won it with a header deep into stoppage time.
Six Burnley men were booked including Gareth Taylor who will now miss any FA Cup replay.
Ian Moore's third goal in four games gave the Clarets an 18th minute lead at the New Den.
He lashed the ball home from close range having been denied bby Tony Warner from similar range two minutes earlier.
After a turgid start the game livened up but Burnley clung on to their lead at the interval.
It was another easy team selection for Burnley boss Stan Ternent as he sent out the same side for the fifth successive game.
His opposite number Mark McGhee made one change, Christophe Kinet being dropped in favour of young defender Alan Dunne.
MILLWALL 1 BURNLEY 1
Burnley
Beresford
West Cox Diallo Branch
Cook
I Moore Grant Briscoe A Moore
Taylor
Millwall
Warner
Dunne Ward Robinson Ryan
Ifill Wise Livermore Reid
Claridge Harris
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