Brazilian Elano guided Man City to a sixth successive home win.
Elano celebrates his fourth league goal
Elano put the hosts ahead in the latter stages of the first half, cleverly slotting home with a left-footed shot.
If Elano provided the attacking threat - the Brazilian also went close with a second-half shot - the home defence had to weather a gritty Blues fightback.
Goalkeeper Joe Hart twice came to his side's rescue, making a one-handed stop to thwart Olivier Kapo as well as a reaction save to deny Fabrice Muamba.
Watching Manchester City it is hard to imagine this was a club which managed just five home wins last season, testament to the change brought about by Sven-Goran Eriksson's arrival.
Elano, who was one of Eriksson's many summer signings, has lit up the Premiership this season with his eye for a pass and sumptuous ball control, not to mention his goalscoring abilities.
This was his fourth goal in three league games for Eriksson's side, while he had also scored in Brazil's 5-0 midweek World Cup qualifying win over Ecuador.
Showing no sign of jet lag, Elano was quick to establish City's tempo, beautifully flighting the ball into the path of Martin Petrov, who was crowded out by the Birmingham defence.
Just before scoring, Elano went on a mesmerising run that brought him to the fringes of the Birmingham penalty area until his progress was ended by Liam Ridgewell's strong tackle.
If there were furious protests from Birmingham that Muamba was fouled by Michael Johnson in the build-up to the goal, there was no argument about the elegance of Elano's finish.
The Manchester City playmaker was quick to gather Vedran Corluka's pass before guiding the ball into the corner of the net past Maik Taylor's outstretched arm.
Midway through the second half Elano came close to scoring a second when his low shot went narrowly wide.
Equally important for the home side was the way they were able to protect their lead.
While Hart, who was impressive for the England Under-21 side in midweek, continued to futher his reputation with those two saves, Corluka got in some crucial blocks.
Prior to the Brazilian's goal, Cameron Jerome proved Birmingham's most potent attacking threat.
The former Cardiff striker might have done better following a free-kick in the City penalty area after Hart had picked up a back pass, but Jerome's effort was deflected to safety.
Soon after the break Birmingham boss Steve Bruce brought on Daniel de Ridder for Gary McSheffrey to try and reinvigorate his attack and the Dutchman began to trouble Javier Garrido.
While De Ridder probed City's left flank, on the other side of the pitch Wilson Palacios and Kapo combined to set up Muamba, whose shot was superbly saved by Hart.
But City have conceded just two goals at home this season and Eriksson's side held on to secure a fourth clean sheet at Eastlands.
Man City manager Sven-Goran Eriksson:
"I was surprised at the way he shook off the jet-lag.
"He's a great player and is scoring important goals for us.
"The way he took the goal was something to be proud of and I believe Elano can get better."
Birmingham manager Steve Bruce:
"It was a blatant foul, and we feel really harshly treated.
"It was a ridiculous decision. The game hinged on it.
"We gave Elano one bit of space - and he scores. But we did not deserve to get beaten."
Man City: Hart, Corluka, Richards, Dunne, Garrido,
Ireland (Ball 80), Johnson, Hamann, Petrov,
Mpenza (Samaras 65), Elano (Gelson 89).
Subs Not Used: Isaksson, Geovanni.
Booked: Corluka, Garrido, Johnson.
Goals: Elano 37.
Birmingham: Maik Taylor, Kelly, Schmitz (Danns 87), Ridgewell,
Queudrue, McSheffrey (De Ridder 58), Palacios, Muamba,
Nafti (O'Connor 76), Kapo, Jerome.
Subs Not Used: Kingson, Sadler.
Booked: Palacios, Ridgewell.
Ref: Mike Dean (Wirral).