The win lifted Chelsea to within five points of leaders Arsenal, with a game in hand. Derby held out for 25 minutes but once Lampard had converted a penalty there was only one winner and Chelsea stormed to a victory to move up to 61 points, three behind second-placed Manchester United.
Salomon Kalou made it 2-0 and it stayed that way until half-time, but Lampard, Joe Cole and two more from Lampard sealed victory, rendering David Jones's late goal barely a consolation.
Aston Villa were indebted to a contentious second-half penalty as they drew 1-1 at home with Middlesbrough.
Stewart Downing gave Villa a deserved lead in the first half but Luke Young was desperately unlucky to give away a penalty when a shot hit him on the arm as he looked the other way.
Gareth Barry stepped up to take the penalty and made no mistake to give Villa a share of the points, but they are now seven points behind Liverpool and Everton in the race for fourth spot.
In the night's other game, Portsmouth beat Birmingham City 4-2 to go ninth, with Jermain Defoe setting them on the way with two goals inside the first 10 minutes.