Hargreaves drove home a superb 25-yard shot after 18 minutes and was deservedly named man of the match.
Mario Balotelli added a second before the break to secure City's passage into the last 16 and end the holders' interest in the competition.
When Hargreaves released a video on YouTube during the summer of him being put through his paces tied to a treadmill, it seemed like the last act of a desperate man attempting to revive his career.
It turned out to be a masterstroke.
Interest was generated, with West Brom eager to seal a deal, and that in turn led to Manchester City boss Roberto Mancini making his move as the transfer deadline approached, with City clearly not in a position to secure all the midfield targets they were after.
Mancini did not expect anything quickly - and has not even named Hargreaves in his Champions League squad.
However, after virtually three years on the sidelines, punctuated by a couple of very brief appearances, totalling only six minutes of actual playing time, the 30-year-old is clearly a man in a hurry.
First, he got himself ready for action within three weeks. Then, 18 minutes into his debut, he scored.
It was some goal too, seizing on a loose ball as Carlos Tevez and Balotelli had their route into the penalty area blocked and letting fly from 25 yards.
The shot went like an arrow past Birmingham goalkeeper Colin Doyle and into the top corner.
City's fans erupted, bellowing "Fergie, sign him up", just as they did when Tevez crossed the great divide two years ago.
That was a far more acrimonious move. Hargreaves' exit was the only plausible ending after spending so little time on the pitch.
Indeed, the goal was his first since April 2008, one of only two Hargreaves scored in 39 appearances for the Red Devils.
Although it was anticipated Hargreaves would be replaced at the break, the former England man re-appeared and lasted for another 12 minutes before departing to a standing ovation.
The good news is a previously stellar career is on the move again and Hargreaves will not need to get back to his peak for England manager Fabio Capello to take an interest given the dearth of top-quality defensive midfield men in the Premier League.
Balotelli could never be described as a forgotten man.
The Italian has tended to be overlooked though, as Edin Dzeko and Sergio Aguero went on their early-season scoring blitz.
With Tevez dropping deep, Balotelli was the focal point of City's attack and when Aleksandar Kolarov crossed from the left seven minutes before the interval, the former Inter Milan man neatly swept home his first goal of the season.
It was a good night all round for City as Kolo Toure also made his comeback after serving a six-month ban for a failed drugs test.
Toure made his mark too, being perfectly placed to clear off the line after Romanian goalkeeper Costel Pantilimon had dropped Jean Beausejour's free-kick, offering Curtis Davies the chance to send an overhead kick towards City's otherwise empty goal.
It was Birmingham's only attack in the first half of their first game in this competition since they stunned Arsenal in last season's final.
What was a joyous Wembley day turned out to be the moment Birmingham's season began to unravel, a process that became so dramatic it ended in relegation to the Championship.
Only Keith Fahey remained from that starting line-up and as manager Chris Hughton made seven changes to the side hammered at Southampton, he clearly feels this is one competition too many in a season where the Blues are also scrapping it out in Europe.
Birmingham were better after the break, without creating anything like the opportunity Toure had turned away.
Doyle denied Tevez and Toure near the end but a Manchester City line-up containing Nedum Onuoha - making his first appearance since chief executive Garry Cook resigned over sarcastic comments about his mother - and Wayne Bridge coasted home.