Two goals from Frank Lampard and one from Florent Malouda lifted Chelsea on to 51 points from 22 matches as they ended Birmingham's unbeaten run of 12 league games.
The victory took Chelsea back into first place after seven days in which Arsenal and Manchester United swapped top spot while they were inactive in the league.
Arsenal, who started the night in second place, had a chance to go top if they matched or bettered Chelsea's performance, but they were held to a goalless draw at Aston Villa and slipped to third with 49 points from 23 games.
It was a miserable night for Arsenal whose 24-year-old Belgian defender Thomas Vermaelen went off in the first half with a suspected broken leg.
"His leg is numb, it might be a nerve, or it might be a fracture of the fibula, we hope not, but we will check it in the morning," Arsenal manager Arsene Wenger said.
Manchester United, who clinched their place in the League Cup final against Aston Villa by beating Manchester City 3-1 on Wednesday, fell to second with 50 points from 23.
Tottenham Hotspur complete the top four on 41 points following their 2-0 win over Fulham on Tuesday.
MALOUDA BOOST
Chelsea, who had won their previous four league and cup matches scoring 16 goals, took only five minutes to find the net when Malouda headed in a Joe Cole cross.
They doubled their lead before halftime when Lampard controlled the ball and scored with a low shot past Joe Hart and he added his second with another low strike just before the end.
"It was very important that we won tonight, they are a very good team. We played good football for 90 minutes, it's a good moment for us," Chelsea boss Carlo Ancelotti told Sky Sports News.
Birmingham Boss Alex McLeish, whose side were unbeaten for 15 matches in all competitions, said his players were distraught after losing for the first time since October 17.
"They are very upset," he said, "but we got off to a terrible start and that set us back. We are not normally as defensively poor as we were on that first goal."
Arsenal could find no way past Villa despite both sides going close to scoring.
Villa manager Martin O'Neill said that since losing 3-0 to Arsenal a month ago, his team had not got the points they deserved.
"I hope that turns in the next few weeks. Although we haven't scored for the last four league games we are making chances, and their goalkeeper kept them in it tonight with some great saves."
Improving Everton beat Sunderland 2-0 at Goodison Park with goals from Tim Cahill and Landon Donovan to climb up to ninth.
Blackburn moved up to 11th with a 2-1 win over Wigan Athletic.
