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.
City top the table with 60 points from 25 games, two ahead of United while toothless Villa are looking anxiously over their shoulders down in 15th.
"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."
Mancini, whose side went into a league game not as leaders for the first time since October, was thrilled.
"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.
Carlos Tevez could be making a surprise return to City after a January move fell through and Mancini softened his opposition to a player who refused to warm up as a substitute in a game in September.
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.
Lescott was watched by caretaker England coach Stuart Pearce, who dashed down the motorway having earlier witnessed West Bromwich Albion maul Wolverhampton Wanderers 5-1 away.
Nigerian striker Peter Odemwingie scored a hat-trick as West Brom moved further away from danger and left their beleaguered local rivals inside the drop zone.
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 under increased pressure as the boos rang out at fulltime.
Odemwingie's deflected effort put West Brom ahead before Steven Fletcher's superb turn-and-shot on the stroke of halftime brought the hosts level.
Jonas Olsson's shot slipped through Wayne Hennessey's hands to give the visitors the lead and West Brom then ran riot with Odemwingie's second and third coming either side of former Wolves man Keith Andrews netting on his debut.
