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.
"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.
"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.
"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."
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."
