Trezeguet put Villa in front in the first half but Andy Robertson headed the equaliser in the 87th minute and Mane won it in time added on.

Liverpool manager Juergen Klopp said his side made it difficult for themselves but deserved the victory.

"Of course, it is lucky when you score these (late) goals but I think if you watch the game, then I think if one team deserved to win it then it is us," he said.

Champions Manchester City kept the gap at six points as they too came from behind to beat Southampton 2-1.

Chelsea went third after they won 2-1 at bottom side Watford in the day's late game.

James Ward-Prowse put Southampton ahead early on but Sergio Aguero equalised and Kyle Walker won it for the hosts three minutes from the end of the 90.

Sheffield United moved fifth after a 3-0 win over Burnley while Bournemouth, Newcastle and Brighton also claimed victories.

Liverpool looked set for their first league defeat since January 3 - and their first defeat in 28 league games - after Trezeguet's first-half goal at Villa Park.

Roberto Firmino had a goal ruled out by VAR for offside and Villa defended stoutly until the 87th minute when Robertson headed in an equaliser from Mane's cross.

And Mane then ensured Liverpool took all three points by snatching the second goal in injury time.

Just over a week after shipping nine goals at home to Leicester, Southampton took a shock lead at Manchester City when Ward-Prowse found the net after 13 minutes.

City dominated possession but it took them until the 70th minute to equalise as Aguero made it 1-1 with the home side's first shot on target.

And as the pressure told on Southampton, Walker popped up with the winner in the 86th minute to keep City in touch with the leaders.

City manager Pep Guardiola said his side threw everything into attack and it paid off.

"We were so patient. We were aggressive. The rhythm was high from the first minute. Big compliments to the team; it was not easy and we did it," he said.

John Lundstram scored twice as Sheffield United, promoted to the Premier League in the summer, beat Burnley 3-0 to move into the top six.

Arsenal stayed fifth after a 1-1 draw with Wolves while Bournemouth are seventh after a 1-0 win over Manchester United in the lunchtime kick-off.

In a match played in gusting winds, Josh King won it for Bournemouth with a brilliant goal on the stroke of halftime, to leave United down in 10th, 18 points behind leaders Liverpool.

Brighton moved into the top half after a 2-0 win over Norwich, while Newcastle won 3-2 at West Ham to move away from trouble.

Australian Associated Press