One-time Liverpool striker Anelka scored after an hour of a tight encounter before Malouda's injury-time hit secured the points and lifted Carlo Ancelotti's men back to the top of the Barclays Premier League.
 
The Reds are now six points off the pace despite more than matching one of their title rivals in their own backyard.
 
Rafa Benitez went into this, his 25th encounter with Chelsea as Liverpool manager, with midfield general Javier Mascherano back in the fold following a hamstring niggle which kept him out of the 2-0 defeat in Florence.
 
The Argentina captain didn't waste any time proving how crucial he is to Liverpool during a cagey opening. It was a game of cat and mouse, with both sides seemingly content to play the role of mouse. Whenever Chelsea did look to probe, Mascherano was at their ankles, breaking up play and distributing to a red shirt.
 
It took 19 minutes for either side to muster a shot of note, and even then it was a speculative hit from Albert Riera which strayed over.
 
It was another six minutes before the hosts responded in kind when Anelka broke down the right and centred towards strike-partner Didier Drogba, who couldn't produce enough power to beat Pepe Reina with a looping header.
 
Anelka was proving a nuisance against his former club, and it was he who tested Reina with a low header from Michael Essien's cross just before the half-hour mark.
 
Down at the other end Steven Gerrard attempted to worry stand-in stopper Henrique Hilario with a bending free-kick from the edge of the box, but his effort looped narrowly over the bar.
 
The first goal was going to prove crucial, that much was already clear. It almost came through Michael Ballack with a near post header from Deco's dead ball, but the German was left head in hands after finding the stands.
 
Chelsea again came close when Essien collected a Martin Skrtel cross before striking the ball low and hard. Reina was on his toes to save but finally the game was opening up.
 
With half-time approaching Liverpool mounted a break down the right, Dirk Kuyt crossing to the head of Fernando Torres, who like Drogba before him couldn't find the thrust to trouble the goalkeeper.
 
During Liverpool's last visit to Stamford Bridge, Petr Cech was duped by a cunning free-kick from Fabio Aurelio as Liverpool took the initiative. The trick was almost repeated by Albert Riera from 40 yards, but Cech's No.2 was at his very best to keep the scores level going into the break.
 
Liverpool began the second half well, with Kuyt using the run of Glen Johnson to find a yard to cross. The Holland international picked out Gerrard 12 yards from goal, but the skipper's header veered marginally wide into the hoardings.
 
Gerrard was starting to make his presence felt. For his next trick the No.8 thundered towards the top corner from the edge of the box. Just over.
 
For all this pressure, Liverpool couldn't dent the scoresheet, and they found themselves behind on 60 minutes when the otherwise excellent Mascherano lost possession in midfield. The ball came to Drogba down the left and the Ivorian delivered a superb cross for Anelka, who got beyond Emiliano Insua to sidefoot over Reina.
 
Benitez responded by introducing the in-form Yossi Benayoun for Riera. The Israeli was soon making an impact, robbing Drogba of possession before winning a corner which came to nothing.
 
Next he turned Deco before feeding Glen Johnson for a punt from 25-yards. The former Chelsea man's aim was askew but he almost made up for it immediately with a neat throughball for Torres. El Nino in turn looked for Gerrard but no one in a red shirt attacked the ball and Essien was on hand to clear up.
 
Liverpool pushed and pushed, Torres volleying wide from 10 yards. More frustration.
 
In the end it was Chelsea who extended their lead after Drogba broke free in the box and centred for Malouda to tap home.