Tony Philliskirk's side extended their unbeaten run to six matches, after a 0-0 draw in the Capital.
In testing conditions, Burnley looked the brighter side out of the two and came close when Will Harris fired an effort just wide early on.
Jayden Major then forced a couple of corners, with two close range efforts in the first-half.
Millwall's first real opportunity came when a strike was rifled just wide of the post.
And the home side came out the blocks early on in the second half, seeing two good chances missed.
However, Harris - fresh from signing a one-year extension with the club three days earlier, then forced Millwall's goalkeeper into a smart save to keep the scores level.
Clarets stopper Harry Allen was then forced into action, after saving a free-kick to his right to keep the hosts at bay.
And despite Millwall's late pressure, Philliskirk's side held on to secure a point away from home and remain unbeaten in the calendar year.
The Clarets are next in action against QPR on March 16th at the Barnfield Training Centre.