Chelsea stormed back to the top of the Premier League with another superb home performance as they ended Birmingham's 15-match unbeaten run in fine style.
Florent Malouda got the ball rolling with the simplest of headers after some good work down the right by Joe Cole.
And Frank Lampard grabbed the second with a typically pin-point 20-yarder.
Birmingham had only two shots on goal, Petr Cech saving the best from Keith Fahey, and Lampard slammed in a third late on to wrap up a comprehensive win.
The results means the Londoners, thanks in part to rivals Arsenal's failure to beat Aston Villa at Villa Park, return to the top of the table after falling off the number one spot last weekend for the first time in three months.
McLeish deflated after defeat by Chelsea
And with key striker Didier Drogba due to return to the squad this weekend following the Ivory Coast's exit from the Africa Cup of Nations, the Blues' title rivals could not possibly underestimate the challenge Chelsea pose in such apparently irrepressible form.
Not that Chelsea have missed the frontman's presence, as they have scored 17 goals in the four matches they have played without him.
This, too, was a performance full of intent from the hosts, and against one of the most in-form sides in the Premier League.
Had they held out against Carlo Ancelotti's side, Birmingham would have equalled Nottingham Forest's record of of 13 matches unbeaten for a newly-promoted side in the top flight - set in 1994-95 season.
But resisting a Chelsea outfit that has won 31 out of 33 points available at Stamford Bridge this season, including a 7-2 rout of Sunderland last time out, was always going to be a difficult proposition.
The visitors simply had no answer to Chelsea's passing and movement. With Deco the fulcrum, Lampard typically effervescent, and Joe Cole always inventive, Birmingham were given barely a glimpse of the football all night.
And the visitors' task was made all the more difficult by Malouda's early goal.
Joe Cole, in arguably his best performance since his return from a knee injury, created it, beating Lee Bowyer for pace down the right and then crossing to present Malouda with the easiest task of heading home unmarked from six yards out.
Cameron Jerome saw his shot deflected narrowly over the Chelsea crossbar off his strike partner Chucho Benitez at the other end, but the hosts' dominance was otherwise complete.
Joe Cole twice went close with long range efforts, Ballack stung the palms of keeper Joe Hart, and Ricardo Carvalho slammed a header against the post from a Malouda corner as the Londoners toyed with Birmingham at times.
So it was no surprise when Chelsea doubled their lead, Lampard finding plenty of room on the edge of the box, taking a touch, and then slamming precisely into the far corner.
It prompted a slight relaxation in the hosts' approach, allowing Birmingham a rare spell in possession, but Ancelotti's men were back on their mettle at the start of the second half and Ballack, twice, threatened a third.
First he brought a smart stop from Hart with a neat header from Ashley Cole's cross and then his clever flick from Malouda's corner drifted narrowly over.
Birmingham, though, have been nothing if not resolute this season, and twice in a couple of minutes they forged chances out of nothing with the minutes ticking down.
James McFadden should have done better when he dragged wide of Cech's goal from inside the box, before substitute Fahey brought a flying save from the Czech keeper moments later when his toe-poke looked to be heading into the top corner.
It was an admirable, albeit brief, rally from the visitors but it served only in focusing the Chelsea players as they entered the closing stages.
And few could argue that Chelsea did not deserve the third when it came, Lampard striding on to Malouda's pass and firing low past Hart with barely a minute left on the clock.
It means Birmingham stay eighth in the table, though they need feel no shame in succumbing to a superb Chelsea performance.
As for the hosts, an 11th clean sheet of the season only added to a fine night at Stamford Bridge as they march forward in their attempts to win the league title for the first time since 2006.
Chelsea manager Carlo Ancelotti: "We use all the pitch to attack and so Frank is able to run into the box to score. I think he's the best running midfielder in the world. He has this fantastic quality to time his run into the box.
"It's good we are back at the top. We have one more point with a game in hand on United and two points more than Arsenal.
"That's important because on Sunday United play Arsenal. Maybe we can improve our position on Saturday."
Birmingham boss Alex McLeish: "I don't think anyone has won here this season and they have battered better teams than us.
"I'm not disappointed with the players at all. They deserve tremendous credit for the run they have been on and they have the character to bounce back.
"Chelsea are a good side. They have the foreign flavour, the keep-ball and movement is excellent. They are one of the favourites for the Champions League, let alone the Premier League.
"We have kept the ball better than that and were wasteful in possession, but I'll forgive the players this one. There's no disgrace losing here."
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