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Chelsea's Diego Costa in action on October 17, 2015.Tony O'Brien/Reuters

Chelsea and Manchester United bounced back from disappointing losses with impressive wins in the Premier League on Saturday.

Diego Costa, returning from a three-match suspension for violent conduct, put the Premier League champions ahead against Aston Villa at Stamford Bridge, before defender Alan Hutton scored an own goal in Chelsea's 2-0 win.

A victory was welcomed by Jose Mourinho, who is under pressure due to his side's faltering start to the season. Chelsea lost its last match 3-1 at home to Southampton and Mourinho feels his team still has work to do to return to top form.

"Confidence comes with results, and results bring all the good quality that the players have to the fore," Mourinho said. "At the moment, some of my players have lost confidence but this was a great team performance."

United won 3-0 against Everton at Goodison Park, with Morgan Schneiderlin, Ander Herrera and Wayne Rooney scoring in an emphatic response to the 3-0 defeat against Arsenal two weeks ago.

"The defeat against Arsenal, two weeks and I cannot approach them (during the international break), then this performance? Fantastic," United manager Louis van Gaal said.

United is third on 19 points, two behind Manchester City, which routed Bournemouth 5-1. Raheem Sterling scored a hat trick in the first half and Wilfried Bony netted twice, meaning injured striker Sergio Aguero was not missed.

The two Manchester clubs play each other at Old Trafford next weekend.

"I think it was important for Raheem to score three goals," City manager Manuel Pellegrini said. "He must improve his finishing – he did that today. I don't think he's a striker like Kun (Aguero) or Bony but this year, and I said it when he arrived, I am sure he will score more goals."

Earlier Saturday, Juergen Klopp's first Liverpool match ended 0-0 against Tottenham.

Klopp was without striker Daniel Sturridge, who picked up a knock in training on Friday, so gave a first Premier League start to Divock Origi, who hit the post with a header after 10 minutes.

It was the closest Liverpool came to scoring, while Tottenham's Clinton N'Jie was later denied by a brilliant one-handed save from Simon Mignolet.

"We had our moments. From a very good corner we hit the post and there were some other situations where we could have been a little bit better, but for today it's ok," Klopp said, while also explaining that Sturridge could return for Liverpool's game against Rubin Kazan in the Europa League on Thursday.

"We made a diagnosis and screened him to be sure – we can see a little bit of swelling but nothing really serious. So we have to see. I hope he's ready to play on Thursday," Klopp said.

In the late game on Saturday, Arsenal netted three times in 12 second-half minutes to win 3-0 against Watford at Vicarage Road.

Alexis Sanchez begun the scoring in the 62nd after Mesut Ozil was tackled in the penalty area, only for the ball to roll free.

Giroud then lashed in Ozil's cut-back six minutes later before Aaron Ramsey netted his first club goal of the season, receiving a pass from Hector Bellerin before his effort was deflected by Ikechi Anya.

The result means Arsenal stayed second, above United on goal difference.

Elsewhere, Southampton surrendered a two-goal lead to draw 2-2 at home to Leicester, Sunderland lost 1-0 at West Brom in Sam Allardyce's first game in charge of the Black Cats and Crystal Palace was beaten 3-1 by West Ham.

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