Craig Bryson's first goal at Pride Park set the Rams on their way and fellow midfielder Jeff Hendrick extended the lead before half-time.
Steven Davies added a third goal in the second half to ensure it would be no win in six league matches for Millwall, who have now gone 505 minutes without scoring a Championship goal.
Derby made two changes after claiming the East Midlands bragging rights against rivals Nottingham Forest.
One was enforced with Frank Fielding suspended following his second-minute red card at the City Ground, so summer signing Adam Legzdins made his full debut.
Leading goalscorer Steven Davies was recalled for Tomasz Cywka, who was the unfortunate man to be sacrificed after Fielding was dismissed last weekend.
Millwall manager Kenny Jackett made five changes from the side that started the Carling Cup defeat to Wolves.
Goalkeeper David Forde, defender Paul Robinson and midfielder Liam Feeney and Liam Trotter, all of whom started the goalless home draw against West Ham last weekend, returned to the starting XI after missing out on Tuesday night.
Tamika Mkandawire was absent through injury at Molineux, where Tony Craig deputised in defence. But striker Jay Simpson was recalled against Derby in the only change from the line-up that started against the Hammers.
Hamer Bouazza and Dany N'Guessan both had a couple of efforts inside the opening quarter of an hour without working Legzdins.
Forde was forced into action, though, in the 18th minute when he had to tip over a shot from former Lion Theo Robinson.
Derby took the lead after 24 minutes. Ben Davies embarked on a driving run to the byline and cut the ball back for Bryson, who scored from 12 yards out despite a handful of defenders on the goalline.
Bouazza continued to look a threat and sent another effort wide just before the half-hour mark.
Ben Davies went close with a long-range shot before setting up Derby's second goal.
His pass from the right-hand side of the area was clinically dispatched by Hendrick, who also scored the second goal for Clough's side at Forest last week.
Robinson might have done better with a header for Millwall before Steven Davies almost showed him how it was done just before half-time. However, his effort hit the crossbar.
Legzdins foiled Simpson with a routine save at the start of the second half before Steven Davies went close with an effort from the edge of the box.
Derby's leading scorer grabbed his fourth goal of the season soon afterwards.
Good work from Bryson and John Brayford created space for Jamie Ward and he teed-up his strike partner who scored from 12 yards.
Steven Davies sent another shot narrowly wide midway through the second half in what was the last meaningful attempt on goal from both sides until N'Guessan fired wide in injury time.