The Lions, who had first-team coach Adam Barrett in charge following Harris' decision to stand down as manager earlier this week, went in front thanks to Jed Wallace's early penalty, which saw Gaetano Berardi dismissed.
Tom Bradshaw's second goal in two games, and first ever goal at home for the club, then doubled the lead.
Ezgjan Alioski reduced the deficit in the first minute of the second period, but the hosts held on to record their first league victory since August and a ninth win in their last 11 home games against Leeds.
The three points sees the Lions climb up to 15th in the Championship, while Leeds drop out of the automatic promotion spots and are down to fifth.
But Millwall did not have to wait long until they were in the lead. Bradshaw got on the wrong side of Berardi and the defender brought him down within 15 minutes.
Referee James Linington wasted no time in pointing to the spot and then giving Berardi his marching orders before Wallace wonderfully dispatched the resulting penalty into the top left-hand corner for his third goal in five games against the Yorkshire outfit.
The Lions continued to swarm Marcelo Bielsa's men and doubled their advantage just before the break. Ben Thompson, who was back in the starting line-up after two games, played a cheeky pass into the path of Shane Ferguson, who drilled across for Bradshaw, who in turn used the pace on the ball to apply the finishing touch with an exquisite flick into the far corner via the post.
Bielsa reacted by introducing Barry Douglas for Helder Costa at half-time, which meant Alioski moved further forward. And that change paid dividends almost immediately as Alioski tapped home Jack Harrison's 46th-minute cross from close range to score just Leeds' second goal in their last six trips to The Den.
Despite being down to 10 men, Leeds applied some late pressure but Millwall stood firm to pick up a much-needed victory in front of their own fans.