Two goals from Florent Malouda and a dazzling individual effort from Salomon Kalou took Carlo Ancelotti's side above Arsenal into second place on goal difference.
Birmingham pulled a goal back through a Sebastian Larsson penalty but Chelsea are now six points behind Manchester United with a trip to Old Trafford to come on May 8.
True Blues: Chelsea moved intot second place with a win over Birmingham City
Ancelotti said: 'It was a good result. Closing a six-point gap with just five matches to go will not beeasy, but our aim is to stay focused and close the season well.
'Everything is open (but) I would like to be in Manchester United's place at this moment.
'If we thought one month ago we had a little chance to come back and fight for the title, everyone could say we were crazy.'
Fernando Torres might even score one day. Ancelotti left his ?50million signing on the bench again for over an hour but said he is 'the present and future' of Chelsea. However, he would do well to copy Kalou after the Ivory Coast forward's sensational effort.
Smash and grab: Malouda (centre) steals in to prod Chelsea in front
With Chelsea back to playing a 4-3-3 formation, and Kalou, Malouda and Didier Drogba in attack, Ancelotti's side showed some of the ruthless, machine-like qualities they exhibited in August. They moved the ball from defence to attack with pace and power, particularly in the first hour.
Remember when it seemed like a secondsuccessive Premier League title was a formality, having scored 12 goalsagainst West Bromwich Albion and Wigan without reply?
Last night's match pitched the leaguechampions and FA Cup holders against the winners of this season's Carling Cup and, with Torres barely settled on the bench, it took Chelsea just three minutes to score.
Flo blow: Malouda (centre) celebrates after opening the scoring for Chelsea
John Terry played a long pass to Paulo Ferreira, who delivered a cross into the six-yard area. Drogba flicked it on and Malouda nipped in front of Stephen Carr to prod the ball home.
Drogba, in particular, looked like a man with a point to prove as he whipped a swerving, right-foot shot in Ben Foster's direction after four minutes. The Birmingham goalkeeper parried the vicious effort, but the way he puffed out his cheeks said itall.
Foster was a relieved man again 20 minutes later, when Drogba attempted to chip him from 35 yards with a right-foot effort. There was another right-foot effort, this time stinging its way past the far post, which had the goalkeeper scampering across his goal-line later in the half.
Clinical: Salomon Kalou (left) fires the Blues into a two-goal lead in the first half
Drogba played the provider again for Chelsea's second goal after 26 minutes, sending compatriot Kalou off on adizzying run across Birmingham's penalty area with a pass he hoped to receive back.
Head boy: Malouda nods his second goal of the night
But Kalou had only one thing on his mind, eluding Roger Johnson and tucking a brilliant right-foot shot intothe bottom corner of the net. His second goal in as many games brought deserved applause from his manager. It really was exceptional.
Birmingham's best two first-half chances fell to Cameron Jerome. If you think Torres has got problems, having failed to score in 725 minutes in a Chelsea shirt, spare a thought for the 24-year-old Birmingham striker. Jerome has not scored inthe Premier League since November, a run stretching 19 games.
He forced a save from Petr Cech after20 minutes and was denied by an Ashley Cole block later in the half butBirmingham, for the most part, looked shell-shocked.
Poor defending, particularly from set-pieces, didn't help their cause. The way Michael Essien was allowed to meet Drogba's free-kick just after the restart was a case in point.
Alex McLeish's side are five points and three places above the relegation zone, but with five matches to play and away fixtures at Liverpool, Newcastle and a final-day trip to Tottenham to come, it will be a nervous run-in.
Johnson looked rueful as he jogged back from a corner having fired a header over. Goal difference could be important come May 22.
Support cast: ?50m signing Fernando Torres started the game on the bench
Birmingham boss McLeish said: 'We got off to a shocking start, and you give yourself a mountain to climb.
'Chelsea are in decent form, but we hung in there and never gave up.
'Anything could happen the way this Premier League has gone this season. I would say we're in a good position (to stay up), with five games to go.'
Worry: Chelsea manager Carlo Ancelotti was forced to withdraw Ashley Cole early in the second half
Torres was applauded as he warmed up,Ryan Bertrand, 21, was introduced first. The England Under 21 defender,who has been on loan at Nottingham Forest, slotted in at left back forhis Chelsea debut.
It took him only five minutes to makean impact as he delivered a beautiful cross for Malouda to score his second goal of the evening and his 13th of the season after 62 minutes.
Consolation: Birmingham got on the scoresheet thanks to Seb Larsson's late spot kick
Torres, the record signing between two British teams, was introduced to the action in the 67th minute with Nicolas Anelka to cries of 'attack, attack, attack' from the home fans.
Chelsea duly reverted to a 4-3-1-2 formation, with Torres alongside Drogba and Anelka just behind the pair of strikers, but it was the new Chelsea signing at the other end who played a more influential role.
David Luiz, a ?25m signing from Benfica, brought down Birmingham substitute Matt Derbyshire to give awayhis second penalty since joining Chelsea in January. Larsson duly converted with a fine spot-kick.
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