Carlos Tevez scored late to give Manchester United a 1-0 win at 10-man Stoke on what looked like a tired return to the English Premier League by the defending champions yesterday.

United were far from its best after winning the Club World Cup in Japan and had rarely troubled Stoke until seven minutes to go, when Tevez scored from close range after a pass from Dimitar Berbatov.

The victory was the first by one of the so-called 'big four' for 20 days, with Liverpool, Chelsea and Arsenal all having gone winless since United departed for Japan.

Post-Christmas games

Liverpool and Chelsea, though, soon emulated United by winning their first post-Christmas games.

Liverpool stayed top of the standings with a 3-0 win over Bolton, while Chelsea beat bottom-placed West Bromwich Albion 2-0 to remain a point back in second.

Aston Villa strengthened their grip on joint third place by clinching a 2-2 draw in injury time against Arsenal, their nearest challenger for the final Champions League place.

United moved up to third place and remain ahead of Villa on goal difference.

"At this stage of the season, they are all big wins when you get them," United manager Alex Ferguson said. "Sometimes, you have to be patient in games like this. It was worth it to get three points."

Robbie Keane scored twice to lead Liverpool to victory over a stubborn Bolton and secure a Premier League win at Anfield for the first time in four games.

Albert Riera had put Liverpool ahead in the 26th before Keane's second-half goals.

Didier Drogba, who finally started up front alongside Nicolas Anelka and Frank Lampard scored in the first half for Chelsea to take the Blues to 41 points - albeit from two more games than United.

Powerful header

"We are delighted to have Didier back," Chelsea assistant manager Ray Wilkins said. "It is always nice to score early on and it was a classic centre forward's goal: A powerful header."

At Villa Park, Denilson and Abou Diaby looked to have sealed Arsenal's victory as they led 2-0 by the 49th in a pulsating match.

But Gareth Barry converted a penalty in the 65th before defender Zat Knight struck in injury time to leave the Gunners 10 points behind leaders Liverpool.

"I feel in the second half they were never really dangerous and yet we conceded two goals in the half where we were never really troubled," Arsenal manager Arsene Wenger said.

West Brom stayed last with 15 points, while West Ham climbed away from the relegation zone with a 4-1 win at Portsmouth.

Craig Bellamy, who was subject to a bid by Tottenham on Wednesday, scored the Hammers' third and fourth goals.

Climbed out of relegation

Spurs stayed 16th after a 0-0 draw against Fulham, who are now on their best ever Premier League run of eight unbeaten matches, while Manchester City climbed out of the relegation zone - to be replaced by Stoke - with a 5-1 win over Hull. Felipe Caicedo and Robinho each scored twice by the 36th minute, before Stephen Ireland got City's final goal with eight minutes left after a sweeping passing move.

Also, Everton won 1-0 at Middlesbrough to take sixth place and Blackburn drew 0-0 at Sunderland.