Carlo Ancelotti's side took advantage of Arsenal's failure to beat Tottenham to leapfrog Arsene Wenger's team and revive their hopes of retaining the title in the process. The champions are six points adrift of leaders Manchester United with five games remaining and Chelsea must travel to Old Trafford on 8 May when they will have the opportunity to strike a further blow against Sir Alex Ferguson's side.
"If we thought that one month ago we'd have a little chance to come back to fight for the title, I think that everyone could have said we were crazy," said Ancelotti. "Now we are happy because we've reached second place. We await to see what happens in the next five games.
"We know United have to play against Arsenal. Everything is open. Obviously, I would like to be in United's position, six points ahead. That's a lot at this stage of the season."
This was a routine victory for Ancelotti's men, with Birmingham's solitary goal coming from the penalty spot when Sebastian Larsson converted after the home side had already established a three-goal lead.
Fernando Torres was again left on the bench by Ancelotti and failed to score his first Chelsea goal after being introduced as a 67th minute substitute. Ancelotti had voiced his support of Torres before this game, expressing his confidence that the striker would soon be celebrating his first Chelsea goal. But the Italian's team selection made it clear his priority lay not with nurturing a misfiring £50million forward back to form, but building on Saturday's win at West Bromwich Albion.
Torres was joined among the substitutes by Nicolas Anelka while Didier Drogba led the line, flanked by Malouda and Kalou. And it was impossible to fault Ancelotti's judgement as his side established control of this game long before the half time whistle to maintain the pressure on the top two.
Even so, there was no excuse for the weak Birmingham defending that allowed Malouda to put the home side ahead in the third minute. Paulo Ferreira collected a cross-field ball and had time and space to deliver a cross to the near post where Drogba headed on and Malouda scrambled the ball home from close range.
To their credit, the visitors responded positively, enjoying long periods of possession and working the ball around the pitch comfortably. Alexander Hleb had criticised his team's play this week when he announced he had no desire to stay at St Andrew's after spending the season on loan from Barcelona. He had no one to blame, however, for his failure to make more of a good chance, allowing John Terry to snuff out his clear run on goal.
An even better opening for the visitors came in the 20th minute when Barry Ferguson's long ball released Cameron Jerome, whose shot was tipped wide by Petr Cech.
Chelsea, though, were giving the impression they were playing within themselves and when Kalou injected a moment of individual skill into the clash, it was effectively game over. The Ivorian has been a fringe player this season, but he demonstrated his quality when he collected the ball with his back to goal, evaded two tackles and curled an excellent drive inside the post in the 26th minute.
Needing two goals to get back into the game, Birmingham had to respond quickly but Chelsea grew in confidence and rarely looked in danger of letting the lead slip. Malouda headed substitute Ryan Bertrand's left wing cross beyond City keeper Ben Foster to make it three in the 62nd minute and put the result beyond doubt.