Premier League: Wins for Manchester City, Chelsea and Aston Villa

Pep Guardiola's side beat Sheffield United to close within two points of leaders Liverpool

Manchester City's Spanish midfielder Rodri celebrates with teammates after scoring the opening goal against Sheffield United. AFP

Manchester City moved to within two points of Premier League leaders Liverpool with a routine win over Sheffield United on Saturday.

Rodri opened the scoring after 14 minutes, with Julian Alvarez doubling the lead on the hour for the 2022/23 treble winners. The in-form Phil Foden assisted both goals as City won their second game since the Club World Cup following their 3-1 win at Everton in midweek.

Manager Pep Guardiola said: "Pleased for the clean sheet, a tough month for us in Saudi Arabia but I think that helped us a lot winning the Club World Cup. We're not top of the league but we're not far away. Mood is good, now we rest a bit and have a few days off.

"We've played these types of games many times, we know and sometimes we handle good sometimes not. Against Villa they played the same system, it's tight and difficult. We didn't concede any set-pieces second half and when Oscar [Bobb] came in we increased tempo in the final third and created chances.

"Phil [Foden] can arrive on the sides and make crosses, which is tough without Erling [Haaland] or he has to move in the small spaces and in the pockets. Like David Silva in the past. Bernardo [Silva] and Oscar too are really good in the small spaces."

Elsewhere, Chelsea survived a late fightback by hosts Luton to win a dramatic match 3-2 at Kenilworth Road and end their four-game losing run away from home.

Mauricio Pochettino’s team looked to be on course for a first away victory since November thanks to a brace from Cole Palmer. His first was a powerful low strike and his second an impudent piece of individual skill, while Noni Madueke scored for the second time in as many games as the visitors sailed into a 3-0 lead.

Luton Town's Ross Barkley, centre, scores with a header against former club Chelsea at Kenilworth Road. AP

But they were pegged back as their former player Ross Barkley capped an impressive individual display with a headed goal. Elijah Adebayo then struck to offer the home supporters hope of a spectacular recovery.

Palmer said: "When I took it round the keeper [for the second goal] I thought the other guy would come across fast, so if I waited a second I’d have time to put it in.

"Hopefully this is just the start. I’m adapting to a new life – my teammates, the city, everything’s new to me – and hopefully I can show more on the pitch."

Meanwhile, Douglas Luiz's late penalty gave Aston Villa a last-gasp 3-2 win over 10-man Burnley.

Leon Bailey's opener was cancelled out by Zeki Amdouni before Moussa Diaby restored Villa's lead. Sander Berge saw red for two bookings but Lyle Foster struck to make it 2-2 before the game was settled by a questionable penalty call as Jhon Duran went down in the box with minimal contact. Luiz kept his nerve as Villa moved up to second in the table.

Wolves eased past Everton with a 3-0 win at Molineux thanks to goals from Max Kilman, Matheus Cunha and Craig Dawson. The Toffees, deducted 10 points by the Premier League for breaching Financial Fair Play, have now lost three in a row to sink back into relegation trouble.

Michael Olise scored twice as Crystal Palace beat Brentford 3-1 at Selhurst Park. The visitors had gone ahead through Keane Lewis-Potter's terrific strike, but Olise's brace and Eberechi Eze's goal sealed the three points for Roy Hodgson's side.

Eze said: "It has been a long time coming, we’ve put in some good performances but haven’t got the results. We know what we’re capable of, especially at home. It’s a good result. Michael Olise’s an incredible player, it’s good to play with players like that on the same wavelength. We know what we’re capable of, we can create chances, it just hasn’t clicked. It showed today and it’s a good result."