Chelsea opened the scoring in style after only three minutes when the ball fell to Lampard on the edge of the box and the England international delicately chipped the ball left-footed over the head of keeper Boaz Myhill and into the back of the Hull net.
Joe Cole then tried his luck with a half-volley from just inside the box but his right-footed strike was comfortably saved by Myhill.
Hull nearly equalised in the 20th minute when Daniel Cousin ran at the Chelsea defence, made space for himself on the edge of the box and hit a low right-footed effort which beat Petr Cech but not the left-hand post.
Chelsea were presented with a great chance to double their lead towards the end of the half when Kamil Zayatte lost the ball to Malouda inside his own box but the Frenchman could only blast his shot over the bar.
Anelka then forced Myhill to make a great save as the Blues striker fired in a shot from the right side of the box that the Hull keeper managed tip over the crossbar.
Hull were awarded a free-kick just before half-time which Geovanni struck with power from 25 yards but Cech was equal to it as he palmed the ball to safety.
Chelsea scored a second goal just after the break when Myhill came out to collect a ball over the top but, with the Hull defenders and the Wales international leaving it to each other, Anelka nipped in to slot the ball into an empty net.
Neat play by Lampard and Anelka then saw Malouda presented with a great chance but he could only fire his shot over the bar.
Malouda did get his goal on 75 minutes however as Ricardo Carvalho played in a clever cross with the outside of his foot towards the unmarked ex-Lyon man who calmly slotted the ball past Myhill from close range.