Following a first half of few chances Anelka broke the deadlock with a goal against his former club on the hour, before substitute Malouda wrapped up the win in stoppage time to put Carlo Ancelotti’s side back on top of the Premier League above Manchester United.
The defeat for Liverpool is their third in the opening eight matches of the season and sees Rafa Benitez’s men stay in fifth position.
Chelsea had the first opportunity of the opening half on 28 minutes when Michael Essien whipped a dangerous cross into the middle and Anelka rose highest to head goal wards, but Jose Reina got down well to his left to save at full stretch.
Michael Ballack then sent his header from Deco’s corner over the top when unmarked in the Liverpool area on 34 minutes.
It took 40 minutes for Liverpool’s first chance but Fernando Torres miss-timed his header from a Dirk Kuyt right-wing cross and Hilario comfortably made the save.
Albert Riera was the closest to scoring in first half stoppage time when his 40-yard free kick was tipped around the post by Hilario.
From the resulting corner Martin Skrtel went down under a challenge from behind by Didier Drogba but his penalty appeal was waved away by the referee.
Chances were again at a premium in the opening exchanges of the second half, before the hosts took the lead on 60 minutes.
Javier Mascherano gave the ball away to Frank Lampard, who sent Deco clear. He played in Drogba down the left side of the area and his cross into the middle found Anelka who made no mistake to fire past Reina.
Ashley Cole did well to block a Steven Gerrard attempt on 75 minutes, while Torres side-footed wide in front of goal nine minutes from time.
The win was wrapped up by Chelsea in stoppage time when Drogba out muscled two defenders to get to the by line and he pulled the ball back to Malouda who bundled it into the net from close range.
Liverpool should have got at least one back when Yossi Benayoun somehow managed to put the ball wide of the post when in front of an open goal with Hilario helpless on the floor. And the Blues keeper then pulled off a fine save to deny Gerrard a goal from distance with virtually the last kick of the match.
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