The England striker, who joined for a club record fee of 18 million pounds from Sunderland on Tuesday, swept the ball home from six metres in the 18th minute after goalkeeper Joe Hart could only push Ashley Young's shot into his path.
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"They always say the first goal is important and we got it early, then defended really well and played really well," the 26-year-old Bent told ESPN.
"It's been a hard week but these are the occasions you enjoy because we have beaten one of the best teams in the country."
Villa manager Gerard Houllier said: "I am pleased for Darren because it's his first goal for us and his first game but I thought the whole team were fantastic and they worked very hard for each other and their spirit of sacrifice was outstanding.
"I must congratulate them for that because we have beaten a very good side."
It was the second time this season Bent has scored the winner in a 1-0 victory over City, having converted a last-minute penalty for Sunderland in August.
BAD DAY
The defeat completed a bad day for City whose title hopes took a knock as Manchester United and Arsenal won earlier.
City slipped from second to third, three points behind leaders United having played two more matches than their arch-rivals.
Roberto Mancini's City, who beat Villa 4-0 at Eastlands three weeks ago, hit the post late in the second half when a fierce drive by Nigel de Jong took a deflection off Ciaran Clark and smacked the woodwork.
Apart from his goal Bent did not have any other clearcut chances in front of watching England manager Fabio Capello but his debut will long be remembered by Villa fans who have not had too much to cheer about this season.
The victory moved them up from 17th to 16th, three points clear of the relegation zone.
It was the third time Bent has scored on his debut for a new club following first-game goals for Charlton Athletic and Sunderland.
