Rovers started brightly, forcing Chelsea to give away three corners in quick succession.
On three minutes, Petr Cech was forced into a smart save and conceded a corner from the left foot of Morten Gamst Pedersen. Ryan Nelsen's free header from ten yards out was then hacked off the goal-line by Lassana Diarra.
But seconds later Chelsea took the lead. Lampard's inch-perfect through ball fed Drogba, who outpaced Stephane Henchoz and let fly a low left-footed shot from the edge of the Blackburn penalty area.
The ball went across the body of Brad Friedel and into the far corner of his goal.
Andriy Shevchenko almost made it two when he latched on to a Lampard pass, but his shot on target was weak and Friedel easily held it.
On 16 minutes, Chelsea could have scored twice. First, Friedel made a miraculous one-handed save Shevchenko and followed that by watching the ball zip past him and to safety from Mikel's angled effort.
Blackburn almost equalised on 20 minutes when Benni McCarthy was first to a David Bentley free-kick. The South African striker's header was just wide of Cech's right post.
Michael Essien produced an athletic piece of defending on 28 minutes to deny Matt Derbyshire a certain shot on goal, tackling the livewire striker deep inside the penalty area.
Seconds later and the forward again cut the Chelsea defence in half and sent in a low shot past Cech. This time Chelsea escaped when Ricardo Carvalho sliced the ball clear from just in front of the line.
The pulsating half then saw Chelsea counter-attack on 32 minutes leaving Drogba to chest the ball down and send in a low right-footed drive. Again Friedel was equal to the task and smothered the effort.
Shevchenko could have sealed it for the champions on the stroke of half-time, but he failed to direct his header from eight yards out beyond the impressive Friedel.
Chelsea almost scored in the first attack of the second half. Again Friedel produced a fine save from a diving Michael Ballack header after good set-up play by Diarra.
Chelsea suffered the loss of Ashley Cole on 52 minutes when he appeared to twist his left ankle chasing down a ball. He was replaced by Wayne Bridge.
Shevchenko should have added a goal to an outstanding game on 61 minutes but once again Friedel choose the right direction to dive to prevent the Ukraine striker.
Quite how Chelsea failed to net number two on 64 minutes is anybody's guess as Diarra sent in a fine cross from the right and both Drogba and Ballack failed to add the final touch.
Goal number two eventually came after 67 minutes when a quick exchange of passes with Mikel allowed Lampard to let fly with a trademark 20-yarder which gave Friedel no chance as he buried the ball in the centre of the net.
Lampard and Shevchenko then peppered the Blackburn goal with strikes. but again Friedel prevented certain goals.
Finally Kalou picked up a deft header from Ballack on 90 minutes and slotted the ball home past the hapless Friedel to complete a deserved victory.