United were awarded a spot-kick in the 18th minute but Danny Webber hit a tame penalty, easily stopped on the line by stand-in keeper Henrique Hilario as the Chelsea millionaires took control.
United had survived a frantic opening spell as Lampard tested Paddy Kenny with a stinging free-kick before finding a gaping hole in the Chelsea rearguard.
Republic of Ireland international Alan Quinn, in space on the right pumped the ball towards Webber as full-back Paulo Ferreira headed away for a corner with the ex-Watford striker waiting to pounce.
Drogba scooped another low cross away from the feet of Claude Davis before a Chris Armstrong centre caused chaos in the Chelsea goalmouth. Drogba, still shadowing Davis, leaned on the big centre-back as referee Martin Atkinson pointed to the penalty spot.
Webber stepped forward but his spot-kick was a poor one, third-choice keeper Hilario diving to his left to make a comfortable save.
Quinn slammed a left-foot shot over the top from 15 yards, before Chelsea almost snatched the lead, Drogba flicking the ball to Lampard whose close-range header produced a spectacular reflex save from Kenny.
The Stamford Bridge side finally broke the deadlock in the 43rd minute. Lampard was stopped in his tracks by Mikele Leigertwood, who was booked for the challenge.
The England midfielder slammed in a free-kick from 30 yards , the ball flashing through the wall and wrongfooting Kenny, who dived too early as the ball bounced in front of him.
Chelsea grabbed a second on 49 minutes, Lampard crossing from the left flank for Michael Ballack to head past Kenny from close range.
Lampard flashed a right-foot effort wide of the far post and Arjen Robben had a shot blocked as the London side looked for a third to kill off the game.
Ballack showed his quality with an eye catching right-foot volley from 16 yards, before Rob Hulse almost put United back in the game running on to a Quinn cross to power a header over the top.