Kalou extended their lead in the second half to narrow the gap to two points at the top of the Premier League table.
Chelsea got off to the perfect start by taking the lead after only six minutes.
Michael Essien raced forward and slipped a pass to Nicolas Anelka on the right.
He swept it into the area and City skipper Richard Dunne got his bearings wrong, toe-poking his attempted clearance beyond goalkeeper Joe Hart.
Kalou extended Chelsea’s lead on 53 with a cool finish.
He latched onto a through ball from Essien and rounded Hart to find the corner for his 11th goal of the season .
Anelka almost added a third only for his header to come back off the bar following a cross from Frank Lampard.