Mahrez and Sterling goals help Manchester City see off gritty Everton challenge

Riyad Mahrez and Raheem Sterling struck in the final 19 minutes as champions Manchester City claimed a hard-fought 3-1 win over spirited Everton.

Gabriel Jesus put City ahead at Goodison Park but the hosts did not look like a side that had lost three of their last four Premier League games and hit back through Dominic Calvert-Lewin after he got the final touch on a goalbound effort from Séamus Coleman.

Both sides then had further chances but it was City who secured the points after Mahrez beat Jordan Pickford with a low free-kick and Sterling struck via the woodwork.

The result ensured City remained five points behind leaders Liverpool.

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Ireland international Matt Doherty was on target as Wolves earned a long-awaited first Premier League win of the season and left Watford still searching for theirs.

Doherty's strike and a Daryl Janmaat own goal ensured it was Nuno Espirito Santo's side who broke their duck with a 2-0 success and climbed out of the bottom three, while the Hornets remain at the foot of the table.

Doherty's goal came on 18 minutes. Good link up play involving Joao Moutinho, Jonny and then Pedro Neto – making his first Premier League start for the club – saw the debutant find Doherty's run with a brilliant low cross and the wing back tapped the ball home.

West Ham climbed up to third place with a 2-2 draw at Bournemouth.

The Hammers, seeking to bounce bounce from their midweek Carabao Cup mauling at Oxford, went ahead through Andriy Yarmolenko’s third goal of the season after 10 minutes.

Bournemouth levelled when Joshua King’s 17th-minute goal was allowed to stand after a long VAR check for offside, and West Ham then saw goalkeeper Lukasz Fabianski forced off with an injury.

Callum Wilson's fifth goal in four league games straight after the restart put Bournemouth in front and Nathan Ake saw his effort ruled out by VAR.

Manuel Pellegrini's side secured a point when Aaron Cresswell struck for the second successive game after 74 minutes.

Tottenham moved up to fourth spot with a 2-1 home win over Southampton, despite playing for an hour with 10 men.

Summer signing Tanguy Ndombele put Spurs ahead after 24 minutes with his second Spurs goal.

Serge Aurier was sent off for a second bookable offence seven minutes later, and it was looking bad for Spurs when the in-form Danny Ings pounced on a Hugo Lloris error to level.

But Harry Kane restored Tottenham's lead two minutes before half-time and Spurs held on for a memorable victory.

Frank Lampard enjoyed his first home league win as Chelsea manager with a 2-0 victory over Brighton.

Jorginho coolly converted a 50th-minute penalty after Mason Mount was tripped by Adam Webster.

Willian’s deflected strike secured the three points, the Brazilian’s first goal since March, 14 minutes from time.

Aston Villa stay in the relegation zone after an eventful 2-2 home draw with Burnley.

VAR disallowed a John McGinn goal for offside but Anwar El Ghazi gave Villa a 33rd-minute lead moments later.

Substitute Jay Rodriguez put Burnley on level terms with a header before two goals in the final 10 minutes.

McGinn did get on the scoresheet with an 80th-minute volley but Chris Wood headed home two minutes later to earn Burnley a point.

Crystal Palace beat Norwich 2-0 at Selhurst Park to move into the top 10.

Luka Milivojevic marked his 100th appearance for the Eagles with a 21st-minute penalty and Andros Townsend wrapped up the points in stoppage time.