The France international struck first in the 60th minute when he finished off a sublime low cross from Didier Drogba as Chelsea defied their critics with a performance of grit and quality. Substitute Malouda sealed the win in injury-time when he slid home another low cross from Drogba.
Carlo Ancelotti's side were desperate to get back to winning ways in the league after their 3-1 drubbing by Wigan last week and a lacklustre victory over Apoel Nicosia in the Champions League in midweek.
But it was Liverpool who had the best of the early exchanges and the game sparked into life in the 12th minute when Fernando Torres was fortunate not to receive a yellow card for a late challenge on Chelsea captain John Terry. The Spaniard's right foot was clearly too high and raked the shins of the England defender.
However, referee Martin Atkinson opted to give the Liverpool striker a lengthy lecture, much to the annoyance of the home fans.
Liverpool continued to dominate but a shot from Albert Riera was high and wide of the target in the 19th minute.
Chelsea vs Liverpool (2-0) Full Highlights, FA Premier League (4-10-2009)......
