Malouda opened the scoring on three minutes at Stamford Bridge when he met Didier Drogba’s flick-on to beat Ben Foster, and Drogba almost doubled their advantage but was denied by a fingertip save from the Blues goalkeeper.
Salomon Kalou did add a second when he raced past Roger Johnson and Stuart Parnaby to fire in off the inside of the upright midway through the first half, and Malouda then made it three just after the hour mark when he got away from Liam Ridgwell to head home his second.
The visiting supporters were given something to cheer when Sebastian Larsson converted a penalty after David Luiz fouled Matt Derbyshire, but Chelsea had done enough to take all three points and leapfrog Arsenal in the table after the Gunners drew 3-3 at Tottenham.