Carlo Ancelotti's side opened up a two-point gap over second placed Manchester United. But perhaps more importantly, the victory over another of the main title contenders restored the Blues to winning ways after their 3-1 defeat at Wigan last weekend.
After a tight first half, former Liverpool striker Anelka opened the scoring when he converted Didier Drogba's cross. Drogba was the provider again in stoppage time as he over-powered Jamie Carragher and crossed for Malouda to slide home.
Defeat leaves Liverpool six points behind Chelsea and Rafa Benitez's side have now lost three times in their first eight league games after losing just twice through the whole of last season.
Chelsea were without first-choice goalkeeper Petr Cech, who served his suspension following his red card against Wigan, so Hilario was between the posts.
But while Ancelotti's side were without Cech, they were buoyed by the return of Drogba.
The Ivory Coast striker missed the 1-0 win in the Champions League over Apoel Nicosia in midweek owing to his European ban.
Drogba's value to Chelsea is best illustrated by his return of six goals in seven league games going into this fixture.
And here he looked invigorated after his break when he chased down Deco's through-ball in the third minute forcing Carragher into a last-ditch tackle.
Although new to the English league, Ancelotti is no stranger to Liverpool. The Italian was manager of AC Milan in 2007 when they beat Liverpool 2-1 in the Champions League final in Athens - a victory that avenged Milan's defeat to the Reds in the final of the same competition in Istanbul two years earlier.
Benitez would love to repeat another victory in the Champions League this season and in striker Fernando Torres has a world-class player which would help him achieve it.
Torres, fresh from his hat-trick against Hull, has gone on record saying he is determined to end the club's three-year wait for a trophy.
And his team-mates looked to have taken that message on board as the visitors started this match the brighter with Steven Gerrard whipping in some dangerous crosses from the right.
But it was Chelsea who had the first shot on target in the 25th minute when Jose Reina was forced to save from Drogba's header.
Reina then needed to be alert moments later when Anelka tried his luck with a neat header.
Chelsea midfielder Frank Lampard also tried his luck, but his free-kick from distance was a long way off target.
But just as Chelsea were beginning to find their feet in this match, Albert Riera's free-kick in the 43rd minute nearly squeezed past Hilario at the far post.
After the restart it was Chelsea who looked most likely to make the breakthrough, and so it proved in the 60th minute.
Anelka finished off a neat move after Lampard had disposed Javier Mascherano and fed Deco.
The Portugal midfielder in turn played the ball for Drogba and his cross from the left was perfect for Anelka to poke home.
Drogba came close to adding a second with a long-range free-kick which skidded past Reina's right post.
But substitute Malouda did add a second in the 90th minute when he turned in Drogba's cross at the far post.