Pep Guardiola's men had the match sewn up by half-time at Goodison Park to maintain their 16-point lead at the top of the table and keep alive the prospect of clinching the crown at the Etihad against their bitter rivals.

Leroy Sane opened the scoring with a sweetly-struck back-post volley after only four minutes and Gabriel Jesus soon made it two, scoring moments after Yannick Bolasie had headed a golden chance over for Everton.

Raheem Sterling slotted home the third after fine work from David Silva and the hosts never looked like mounting any sort of fightback, despite Bolasie's second-half consolation.

Second-placed United had earlier coasted to a 2-0 home win over Swansea.

Romelu Lukaku fired the Red Devils in front after just four minutes with a deflected effort and Alexis Sanchez added a second with a low finish in the 20th minute.

Liverpool kept up the pressure on United as they came from behind to win 2-1 at lowly Crystal Palace with a late goal from Mohamed Salah.

The Eagles took the lead through a penalty from Luka Milivojevic after 13 minutes.

Sadio Mane equalised four minutes into the second half before Egyptian Salah secured all three points when scoring his 37th goal of the campaign with six minutes left.

At the other end of the table, West Ham put their recent troubles aside to beat fellow-relegation battlers Southampton 3-0 and lift the atmosphere at the London Stadium.

While there were protests against the board outside Stratford station before the match, there were no repeats of the ugly scenes inside the ground which marred the defeat by Burnley before the international break.

Joao Mario, on loan from Inter Milan, put the Hammers in front after 13 minutes and two goals from Marko Arnautovic, who played under new Saints boss Mark Hughes at Stoke, settled the contest before half-time.

Defeat meant Southampton remained in the bottom three, two points from safety, but the Hammers climbed five clear of danger.

Jermain Defoe came off the bench to net a stoppage-time equaliser as Bournemouth snatched a 2-2 draw at Watford.

Kiko Femenia's deflected volley put the Hornets in front after 13 minutes, but Joshua King levelled from the penalty spot just before half-time.

Roberto Pereyra restored Watford's lead four minutes after the restart only for veteran forward Defoe to have the final say in added time.

Rock bottom West Brom slipped another step closer to relegation after losing 2-1 at home to Burnley.

Ashley Barnes' acrobatic finish put the Clarets ahead after 22 minutes and Chris Wood headed in with quarter of an hour left.

Although Salomon Rondon scored a late consolation, the Baggies were left 10 points adrift of safety with only six games to go.

Newcastle boosted their own survival hopes and dented Huddersfield's with a 1-0 win at St James' Park.

Ayoze Perez struck with just 10 minutes left to push the Magpies up to 12th and leave the Terriers only three points above the drop zone.

Leicester scored two late goals to beat Brighton 2-0 at the King Power Stadium, where they finished with 10 men.

The Seagulls had just seen Glenn Murray's penalty saved by Kasper Schmeichel before Vicente Iborra broke the deadlock after 83 minutes.

Leicester midfielder Wilfred Ndidi was sent off for a second caution with three minutes left but Jamie Vardy slotted in during added time.