The former Reds striker was on hand to slot home the opening goal on the hour mark with the chance being put on a plate by strike partner Didier Drogba's delightful cross.
Drogba was again the provider for the clinching goal in added time as his power was too much for Jamie Carragher, who allowed the Ivory Coast international to square for substitute Malouda to score from close range.
Carlo Ancelotti's men took advantage of Manchester United's unexpected home draw with Sunderland on Saturday evening to move back into pole position ahead of the international break.
Back-up Blues goalkeeper Hilario was rarely troubled by the visitors, although he had to be alert in the first half to keep out Albert Riera's free-kick which looked destined for the bottom corner.
Yossi Benayoun missed a good chance to pull one back in the closing moments before Hilario again proved his ability as he dived to his right to keep out Steven Gerrard's late pile-driver.
Rafa Benitez's men have now sustained three league defeats, one more than they suffered throughout all of last season, and are six points adrift of the leaders with their hopes of ending a 20-year wait for league glory already under increasing pressure.
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 UEFA 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.
DesireLiverpool continued to dominate but a shot from Riera was high and wide of the target in the 19th minute.
Michael Essien appeared to be late and high with a challenge on Javier Mascherano but referee Atkinson was perfectly positioned to see the incident and ignored Chelsea appeals. The Liverpool player soon rose to his feet without any damage to his right leg.
Both sides were full of attacking desire but neither goalkeeper had been tested at the midway stage of the opening half.
Liverpool's Jose Reina finally collected a header from Drogba just beneath the crossbar in the 24th minute but Chelsea's threat was somewhat impotent.
In the 27th minute Reina was called into action again when Essien's cross was met by Anelka. The France international was unmarked but despite the luxury of a free header, he could not find a way past the Liverpool goalkeeper.
Liverpool were handed a chance to open the scoring in the 29th minute when Branislav Ivanovic was adjudged to have brought down Torres.
The free-kick was some 25 yards out but Gerrard's effort sailed over the crossbar to the delight of the home fans.
Four minutes later Chelsea squandered a chance of their own after Drogba had been brought down by Carragher near the corner flag.
Deco's free-kick into the penalty area was well placed but Michael Ballack's header was off target from six yards.
PerfectChelsea were now enjoying their best spell of the game and when Lampard's 38th-minute corner fell to Essien at the far post, the Ghana international forced Reina to make a save at the second attempt.
Liverpool responded with Dirk Kuyt crossing for Torres to head straight at Hilario from six yards.
Deco was booked for a foul on Kuyt in the 44th minute and Riera forced Hilario into a late save with a 40-yard low drive.
In the 57th minute Liverpool won a free-kick when Riera was blocked by Ballack - but Gerrard's delivery was met by a confident punch from Hilario and Chelsea survived a difficult moment.
The Blues broke the deadlock on the hour after Mascherano lost possession to Lampard in the Chelsea half. Essien and Deco fed the ball wide to Drogba on the left - and his centre was perfect for Anelka to convert his fifth goal of the season.
In the 63rd minute, Drogba met Lampard's free-kick but his header was well held by Reina - and four minutes later the visitors replaced Riera with Benayoun.
In the 77th minute Chelsea won a free-kick in a dangerous area when Lampard was brought down by Gerrard. The challenge earned Gerrard a yellow card and Chelsea almost went two goals in front but Drogba was just wide of the right-hand post with his free-kick.
Chelsea's goal was now under siege and Torres wasted a glorious chance to level the scores when he shot wide in the 80th minute.
Substitute Malouda then settled the outcome when he slid the ball home from close range in injury-time, although there was still time for Benayoun to fire wide and Gerrard to force another save out of Hilario.
ChelseaTeam StatisticsLiverpool2Goals001st Half Goals08Shots on Target36Shots off Target93Blocked Shots55Corners815Fouls170Offsides21Yellow Cards10Red Cards077.4Passing Success75.731Tackles3171Tackles Success7152.4Possession47.648.1Territorial Advantage51.9