The former Sunderland player, who joined Villa on Tuesday in a club-record deal, struck with his first clear-cut opportunity after 18 minutes.
With their £59million strike force of Carlos Tevez and Edin Dzeko, the visitors dominated for long spells but struggled to find a way past Villa's rock-solid defence in which James Collins and former City centre-back Richard Dunne were outstanding.
And the result means City are now three points behind Premier League leaders Manchester United and have played two games more.
Villa held on to register only their second win in 11 league games and it lifted them further away from the bottom three.
It also gave them revenge for a 4-0 mauling at Eastlands last month.