Lampard was inches away from giving Chelsea the lead in the 10th minute when his 20-yard shot just evaded the far post.
But Chelsea broke the deadlock in the 20th minute with a goal of classic simplicity.
A Blackburn attack broke down allowing Michael Ballack to collect the ball in midfield.
The Germany captain fed Nicolas Anelka on the left flank with a superb low pass and when the France international crossed the ball into the six-yard box, it was turned past his own goalkeeper by the unfortunate Givet.
Blackburn had to rely on counter-attacks and in the 25th minute they almost grabbed an equaliser but Morten Gamst Pedersen's 20-yard effort flashed wide of Petr Cech's right-hand post.
Chelsea's players were lining up to shoot and Essien tried his luck from 25 yards in the 29th minute but although the ball dipped violently in the air, it still went over the crossbar.
Lampard wasted another chance to increase Chelsea's lead moments later when Ballack's cross found him unmarked on the edge of the six-yard box. But the England midfielder put his header wide of the target.
In the 33rd minute, Rovers goalkeeper Paul Robinson came to their rescue when Lampard fed Anelka inside the penalty area.
A second goal seemed on the cards but Anelka's shot hit Robinson in the chest, much to the frustration of Ancelotti.
It was shooting practice for Chelsea and Robinson did well to punch away a 35-yard blockbuster from Drogba.
Five minutes before the break, Anelka turned and twisted before firing an 18-yard shot into the sidenetting.
Pedersen was the first player into the notebook on the stroke of half-time for a foul on Branislav Ivanovic. Seconds later Robinson pulled off a magnificent save to deny Lampard again.
Chelsea, somewhat predictably, went further in front in the 48th minute through Lampard.
The England midfielder scored his first goal in open play in the top flight since last April when he finished off a fine Chelsea move.
Essien sent Drogba racing into the penalty area and his cross was only half cleared by Lars Jacobsen, leaving Lampard to pick his spot from eight yards.
It was 3-0 in the 51st minute when Essien sent a 35-yard shot thundering beyond the despairing dive of Robinson.
Anelka then tried to repeat the feat in the 54th minute and his 20-yard shot was so fierce that Robinson had to save at the second attempt.
It got worse for Rovers in the 58th minute when Ryan Nelsen brought down Drogba inside the penalty area and Lampard converted the spot-kick for his second of the game.
Drogba underlined Chelsea's superiority in the 63rd minute when he rose highest to head home a corner by Lampard to make it 5-0. It was the Ivory Coast international's eighth goal of the season.
In the 67th minute Chelsea replaced defender Ricardo Carvalho with youngster Jeffrey Bruma for his Premier League debut.
Cole was then replaced by Daniel Sturridge, making his home league debut, in the 76th minute. Cole received a standing ovation from the fans and a bear hug from Ancelotti.
The England midfielder had shown he was back to his best during an afternoon when Chelsea returned to top form.