The Blues dominated throughout and never looked back after Malouda's early effort put them ahead. And, following numerous opportunities to pull further ahead, they had to wait until Anelka struck his 24th goal of the campaign just before the hour to be absolutely certain of the win which moves them to 80 points for the season.
Rovers, who achieved Premier League safety last week, had a few chances without really looking like they would get something from the game.
Chelsea took the lead on four minutes when Anelka's great cross in from the right found Malouda just inside the Rovers penalty area and his thumping header gave keeper Paul Robinson no chance.
The Blues almost went two-up on nine minutes when Ashley Cole's ball in from the left flank set up Anelka in the middle but his effort was straight at the legs of the grateful Robinson.
On 18 minutes Frank Lampard went even closer as he hit a left-foot drive off the Rovers crossbar from the edge of the area after more good work down the right by Anelka.
Didier Drogba almost put a second on a plate for Malouda on 29 minutes when he dinked the ball into the area, but his subsequent chip over Robinson lacked the pace to reach the net before Ryan Nelsen and Gael Givet both combined to hack the danger off the line.
Blackburn had one or two opportunities in the first half, but Blues keeper Petr Cech's only real test was to push a swerving long-range Morten Gamst Pedersen effort round the post just after the half-hour mark.
Rovers had an early chance after the interval when Cech raced out to gather at the feet of Stephen Warnock, who had broke through into the left side of the area.
However Chelsea stepped up a gear to take command with Malouda somehow managing to divert Lampard's ball across the face of the Rovers area back into the arms of Robinson with the goal gaping on 53 minutes.
Cole thought he should have been awarded a penalty on 57 minutes when Keith Andrews pulled him back in the area as he tried to get on the end of Drogba's ball.
Chelsea did get the vital second on 59 minutes when Drogba teed up Anelka to fire in from the edge of the area to move him level with Manchester United's Cristiano Ronaldo at the top of the scoring charts.
Lampard was denied by Robinson on 61 minutes, while Rovers duo Tugay and Warnock had efforts saved at the other end by Cech.
Chelsea almost capped the win with a third in stoppage time when Malouda and then Drogba both had efforts well saved by Robinson.
Match Reports last week