Released by Manchester United in the summer after three injury-ravaged seasons, the midfielder 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 a much-derided competition that will never be dismissed by Hargreaves, as long as the former Bayern Munich man draws breath.
After virtually three years on the sidelines, punctuated by a couple of very brief appearances, totalling only six minutes of actual playing time, Hargreaves took just 18 minutes to open his account for City.
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 Blues goalkeeper Colin Doyle and into the top corner.
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.
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.
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.