The former England international, who has 42 caps, had played less than 15 minutes of competitive football since he last completed 90 minutes exactly three years ago on September 21 2008.
He scored with a superb shot from 22 metres after 17 minutes and was also impressive linking the play and giving City the edge.
They wrapped up their victory with a second from Mario Balotelli after 38 minutes to take their place in the last 16.
Hargreaves was given a rapturous round of applause when he went off, injury-free, after 57 minutes, proving that he had regained his fitness.
"The last three years have been a learning curve for me," he told Sky Sports.
"I could never have anticipated myself being in that position which was trying to make the most of a difficult situation.
"There was a lot of frustration but I met a lot of wonderful people along the way that I would probably have never met, so I can't say it was all bad."
Hargreaves, 30, made just 39 appearances in four years before being released by Manchester United at the end of last season.
He last scored in April 2008 when he hit the winner for United in a 2-1 victory over Arsenal, but within six months a series of injuries left him on the sidelines and with grave doubts about him ever resurrecting his career.
He joined City last month after putting a video on YouTube showing he was over the worst of the problems that have blighted his career.
His new manager Roberto Mancini praised him, telling Sky: "I am happy for Owen because he played well without any problem. He scored a fantastic goal and I hope he can be lucky and stay fit for us in the future."
