Liverpool dominated the early skirmishes in midfield with Steven Gerrard and Fernando Torres linking up well, and although both sides were full of attacking desire, neither goalkeeper had been tested at the midway stage of the opening half.
Liverpool's Jose Reina finally collected a header from Drogba just beneath the crossbar in the 24th minute and shortly afterwards he caught a free header from Anelka. The Reds responded with Dirk Kuyt crossing for Torres to head straight at Hilario from six yards.
The Blues finally broke the deadlock on the hour when Javier Mascherano lost possession to Frank Lampard in the Chelsea half. The Blues made swift work of going forward with Michael Essien feeding Deco and the midfielder passing the ball out wide to Drogba on the left.
For once the Ivory Coast international got the better of Martin Skrtel and crossed low to the far post where Anelka pounced to put the home side in front.
Chelsea wrapped a fine win when Drogba crossed for substitute Malouda to add a second from close range in injury-time.