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Chelsea, Man City, Man Utd and Arsenal all win; Everton lose again

Eden Hazard scored from a header to help Chelsea to a 1-0 win over West Ham and maintain their five-point lead at the top of the Premier League table.

The Belgian winger got his head on a cross from Ramires to hand Jose Mourinho's men the lead in the first half and continue his fine goal-scoring efforts away from home.

Hazard continued to shine in an exciting game after the break and hit the post after linking up brilliantly with Diego Costa, before Ramires' header was brilliantly denied by goalkeeper Adrian's feet and James Tomkins cleared the ball off the line in the final minute.

Manchester City kept up the pressure on Chelsea at the top with a 2-0 win over Leicester.

City struggled to break through in the first-half, but just before the break they broke the deadlock as Aleksandar Kolarov's cross caused havoc in the box and found David Silva. The Spaniard's shot was blocked, but he netted the rebound to score his 10th goal of the season.

City were denied throughout the game by the heroics of veteran goalkeeper Mark Schwarzer, but James Milner struck with two minutes remaining to seal the win.

Manchester United struggled to break down Newcastle but took a 1-0 win from St James' Park.

United had the better of the first half but Emmanuel Riviere could have had a penalty after tumbling after a challenge from Chris Smalling in the box and then watched a shot well saved by David De Gea.

After half-time, Tim Krul came to the rescue for Newcastle with a wonderful double save: first from Marouane Fellaini and then from Ashley Young's rebound. Jonas Gutierrez then returned to first-team action for the first time since October 2013, after recovering from testicular cancer, but was booked two minutes after arriving.

United looked like they might be headed for a draw, but Ashley Young popped up in the final minute to hand his side all three points.

Arsenal failed to get out of first gear but they beat QPR 2-1 thanks to goals from Olivier Giroud and Alexis Sanchez.

In a dull first half, the Gunners could not break through and new signing Gabriel was taken off injured, with Laurent Koscielny replacing him. However, they came out better in the second and Sanchez's fine run and pass found Kieran Gibbs who found Giroud to net his 13th goal of the season.

Sanchez then got himself on the scoresheet in the 69th minute but Charlie Austin got one back for the home side with a thunderous shot from outside the area with 10 minutes to go.

Bafetimbi Gomis collapsed just minutes into Swansea's match at Tottenham as it ended 3-2 at White Hart Lane.

The France striker, a summer signing from Lyon, went to ground as the players made their way to restart after Nacer Chadli gave Spurs an early lead. Gomis was attended to for four minutes and left the field a stretcher, by which point he was conscious and wearing an oxygen mask, with medical staff later revealing that he was "fine."

The game restarted and Ki Sung-Yeung levelled the scores on 19 minutes, but after the break Spurs went ahead against through Ryan Mason and Andros Townsend struck a wonderful shot into the top corner to make it 3-1 before Gylfi Sigurdsson scored a consolation against his old club.

Hugo Lloris then pulled off a stunning last-gasp save to secure all three points.

In the day's late kick-off, Liverpool won 2-0 against Burnley to keep up the pressure on the top four.

The game took some time to get going, but Liverpool took the lead on 29 minutes as Philippe Coutinho's shot was blocked and Jordan Henderson netted the rebound to score for the second game in a row and mark his 200th Premier League appearance in style.

Liverpool then eased two goals ahead as Daniel Sturridge got himself on the scoresheet to keep in the race for the Champions League spots.

Everton's poor form continued as they lost 2-0 to Stoke to ramp up the pressure on boss Roberto Martinez.

A wonderful header from Victor Moses opened the scoring for Stoke in the 32nd minute and the Toffees were unable to get themselves back into the game. Marko Arnautovic hit the post in the 84 minute and Mame Diouf buried the rebound to double the lead and leave Everton in real trouble of being dragged into the relegation battle.