Chelsea leapfrogged Arsenal and moved into second place in the Premier League after brushing aside Birmingham.
Malouda headed in his second at the near post after the break.
Sebastian Larsson scored a penalty for Birmingham after David Luiz fouled Matt Derbyshire but Chelsea held on to cut Manchester United's lead to six points.
With Arsenal dropping two points in a scintillating 3-3 draw across London at Tottenham, the men from Stamford Bridge moved level on 64 points with the Gunners but above them in the table on goal difference.
Chelsea manager Carlo Ancelotti has seen his side win six of their last seven top-flight fixtures and become the form team just as the season moves towards its conclusion.
The west Londoners have five league games left - including a trip to Old Trafford to face United on 8 May - while United boss Sir Alex Ferguson still faces a trip to Arsenal on 1 May.
However, although Wednesday's results might have given Chelsea a glimmer of hope that they can retain their Premier League crown, it was not a perfect evening for Ancelotti's team.
Fernando Torres came on as a second-half substitute for his 13th Chelsea appearance but did not really have a clear sight of goal and has now gone almost 900 minutes without scoring.
There were no such problems for Malouda, who converted the home side's first meaningful attack with a finish from three yards.
The goal came from Paulo Ferreira's right-wing cross after he controlled a raking pass from John Terry.
Ancelotti's men were in total control and almost doubled their lead when Ben Foster struggled to deal with a long-range strike from Drogba that the keeper just managed to tip over his crossbar.
The visiting side did threaten to force their way back into the contest but Terry made a superb covering tackle to deny the recalled Alexander Hleb, who was poised to shoot, while Petr Cech saved Cameron Jerome's strike from a tight angle.
Drogba went close with an audacious attempt at a lob and drew a good save from Foster with a precise strike that threatened to find the bottom corner.
But Foster was powerless to prevent Kalou doubling Chelsea's advantage after the Ivorian capped a fine mazy run that left Roger Johnson and Stuart Parnaby trailing in his wake with a crisp shot from 20 yards that clipped the inside of the post.
If there was any doubt about the outcome of the match, the west Londoners appeared to have made sure of three points when they scored a third just after the hour mark.
Malouda lost marker Liam Ridgewell at the near post and had plenty of time to head a cross from 21-year-old substitute Ryan Bertrand - making his Chelsea debut - beyond Foster.
The visiting side pulled a goal back when Larsson drilled a penalty into the top corner after Luiz had needlessly fouled another substitute, Matt Derbyshire, on the edge of the penalty area as the two players headed away from the danger zone.
And Derbyshire might have pulled another goal back - and in the process set up an exciting climax to the contest - but after bearing down on goal the former Blackburn Rovers player snatched at the chance and his low strike went wide of goal.
Drogba might have capped a fine individual performance with a goal but the striker shot an indirect free-kick from 12 yards over the crossbar after Birmingham had been penalised for a backpass.
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