Alex Neil's side took the lead through Josh Coburn's goal in the 43rd minute at The Den.
Barry Bannan's free-kick wasn't cleared by Derby and Millwall defender Tristan Crama hooked the ball back into the six-yard box, where Coburn glanced his header in at the far post.
That was enough to earn third-placed Millwall a fourth successive Championship victory as they closed the gap on second-placed Middlesbrough to one point.
Derby striker Patrick Agyemang hit the post in stoppage time after earlier missing another golden opportunity to equalise in a second half dominated by the visitors.
Millwall, who have won seven of their last nine games, will hope for a favour from south London neighbours Charlton when they face Middlesbrough on Wednesday.
Fourth-placed Ipswich are three points behind Millwall after a dramatic 3-3 draw at Stoke.
Milan Smit and Bae Junho scored to put Stoke two goals ahead in the first half.
Wes Burns and Jack Taylor dragged Ipswich level before George Hirst gave Kieran McKenna's side the lead.
But Smit converted a stoppage-time penalty to dent Ipswich's push for automatic promotion via a top two finish.
Hull strengthened their grip on a play-off place with a 2-1 win at Wrexham.
Joe Gelhardt and Lewis Koumas scored for Hull, who also missed a penalty from Gelhardt.
Sixth-placed Wrexham, with co-owner Ryan Reynolds watching on, threatened a late comeback as Nathan Broadhead swept home in the 76th minute.
But their rally fell short as fifth-placed Hull made it eight wins from their last 10 away league games.
Vivaldo Semedo's last-gasp equaliser denied relegated Sheffield Wednesday their first win in 31 games as Watford salvaged a 1-1 draw at Hillsborough.