The win puts Chelsea one point clear of Manchester United at the top of the table with a game in hand on their rivals.
The home side went ahead in the fifth minute when Joe Cole burst into the City penalty area from the right flank and crossed for the unmarked Malouda to head past Joe Hart from six yards.
City had been the only team in the league to prevent Chelsea from scoring when the two teams met at St. Andrews on Boxing Day but Ancelotti's side are a different animal at home.
But City managed to stave off the expected Chelsea onslaught by stifling the midfield.
The home side had to wait until the 20th minute for another meaningful attack.
Again Cole sent the ball into the penalty area but it was deflected for a corner.
However, only the width of the upright prevented the home side from increasing their lead seconds later.
Malouda's corner was met by the head of Ricardo Carvalho but the Portugal defender saw the ball cannon back off the post.
Chelsea continued to press and Lampard sent an angled drive into the arms of Hart in the 21st minute, while Cole was inches wide with a 20-yard shot moments later.
Cole was having a fine game for the home side and another 18-yard effort was well held by the diving Hart in the 26th minute.
But Chelsea did make it 2-0 in the 31st minute when Lampard collected a pass from Michael Ballack and sent a low angled drive beyond Hart and into the bottom corner from 20 yards.
Chelsea had now moved up a gear and were in their familiar smooth groove.
In the 34th minute, Nicolas Anelka had a shot deflected for a corner as the home side looked for a third.
Chelsea's passing was fluent and inventive and Birmingham had no answer.
They possessed little attacking threat, with Chelsea captain John Terry proving to be an imposing figure in his 300th career league game.
City had not tested Chelsea goalkeeper Petr Cech and lacked the quality and guile to trouble the home defence.
There was also a distinct lack of ambition in City's play, which was surprising given their 15-game unbeaten run.
Chelsea began the second half with the same attacking desire and a 25-yard drive from Anelka ruffled the side-netting with Hart scrambling to protect his near post.
In the 53rd minute, Hart rescued Birmingham when a cross from Ashley Cole found the unmarked Ballack at the far post.
The Germany captain sent his downward header towards the corner of the net but Hart somehow managed to grab the ball in time.
City replaced Cameron Jerome with Keith Fahey in the 56th minute as the visitors looked to add more impetus to their attack.
Chelsea were inches away from a third in the 59th minute when a corner by Malouda was directed just over the crossbar by Ballack.
Joe Cole deserved a goal as a reward for his performance but he squandered a real chance in the 64th minute when Lampard found him with a fine cross-field pass.
The midfielder, hoping to play his way into England's squad for the World Cup finals this summer, hit a weak shot straight at Hart from eight yards.
Hart was busy again two minutes later when he held a long-range drive from Malouda.
Birmingham's James McFadden broke clear of the Chelsea defence in the 72nd minute but his angled shot flashed the wrong side of the far post.
Moments later substitute Fahey brought a fine save from Petr Cech as City finally put some pressure on the home defence.
But Chelsea made it 3-0 in the 90th minute when Lampard collected a pass from Malouda and fired past the advancing Hart.