Ben Reeves finally breached the rearguard Lions' rearguard, the first goal Millwall have conceded in 10 games, but MK Dons were downed by Lee Gregory.
The striker headed home Shane Ferguson's cross with just 24 minutes on the clock before notching his 14th goal of the season with an injury-time penalty after being brought down in the area.
It was Millwall's fourth penalty award in three games, with Gregory missing two late spot-kicks during a 0-0 draw with Oldham seven days ago, but the 28-year-old dusted himself off to claim all three points.
The Lions now look ahead to their trip to White Hart Lane, coming in eight days' time, as they look to reach the FA Cup semi-finals for the first time since 2013.
Millwall have not beaten Spurs since a 2-0 win in 1939.
"At this stage of the season, it's about winning games," Lions boss Neil Harris told the club's official website.
"It's not about who's the better team, who plays the best football - it's just about getting over the line."