Manchester United's 2-1 win over Liverpool on Saturday had put City under pressure and after they had dominated the first hour's play Lescott eased their nerves when he hooked in former Villa midfielder Gareth Barry's far-post header from a corner.
Adam Johnson also hit a post in the first half for City while Villa threatened little until the final stages when Carlos Cuellar headed over and Hart made a superb point-blank save from Darren Bent.
The England number one's stop, as much as Lescott's goal, could be a moment City fans look back on with glee come May if they get their hands on a first English league title since 1968.
"It's always difficult playing second throughout the weekend," man-of-the-match Barry told Sky Sports.
"[United] obviously put a bit of pressure on, any away game in the Premier League is really tough. But to come to Villa Park is a massive three points for us, we are delighted today.
"We've got to back ourselves now although they are a club who have won many championships recently. We are a team full of experience and have players that have won championships elsewhere. We know what it is all about."
"This evening was a difficult game, we knew this before the game but I think the guys played fantastic football," he said.
Mancini's side lacked a bit of a cutting edge with Sergio Aguero wasteful, David Silva showing his tricks but failing to finish and Edin Dzeko on the bench despite Mario Balotelli's suspension.
Asked if the striker could make a comeback if he apologises, Mancini said: "My reaction is always the same, Carlos knows the situation. It's possible yes. Carlos is a Manchester City player."
The Argentine's reintegration could be a key point in the season but England defender Lescott, a boyhood Villa fan, made his mark by scoring his fifth goal against the Birmingham side to make City's dominance pay having earlier headed wide.
Roy Hodgson's side continued their strong away form to jump eight points clear of 18th-placed Wolves, who endured a fourth straight home defeat to put manager Mick McCarthy u
