Chelsea 2-0 West Bromwich Albion
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Chelsea extended their unbeaten start to the new season to 12 matches, which is a club record.
Their first goal was scored by Diego Costa, who has found the net 11 times in his 10 outings this term.
Visiting West Brom have not won at Stamford Bridge in the league since 1978.
Everton 2-1 West Ham United
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Veteran Everton midfielder Leon Osman scored on what was his 400th appearance for the club.
His goal helped the Toffees to extend their unbeaten run in the Premier League against West Ham to 13 matches.
The Hammers went into the clash having not lost any of their previous six outings.
Leicester City 0-0 Sunderland
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Another shutout means that Leicester have now gone five matches without scoring a goal.
They have also not won a Premier League encounter since September 21, which dates back seven games.
Sunderland have lost none of the three Premier League matches in which Costel Pantilimon has kept goal.
Manchester City 2-1 Swansea City
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The victory was only the second that City have achieved in their last seven outings in all competitions.
One of their goals was scored by Yaya Toure, who found the net for just the second time in the Premier League this season.
For Swansea, Wilfried Bony scored his fifth Premier League goal in six appearances.
Newcastle United 1-0 Queens Park Rangers
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Newcastle's victory was the fifth in the Premier League that they have recorded in succession.
During that run, the Magpies have only conceded one goal, while scoring seven up the other end.
The visiting R's have lost all six of their away matches this season, scoring just twice in the process.
Stoke City 1-2 Burnley
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Having waited 11 matches for their first win of the season, Burnley have now won their last two.
Danny Ings scored both of their goals at the Britannia Stadium, taking his tally to three in four matches.
Stoke had 25 attempts at goal over the course of the 90 minutes, but only three of them were on target.
Arsenal 1-2 Manchester United
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The North Londoners have defeated United just once in the last 15 meetings between the two sides.
The 17 points that Arsenal have amassed from their first 12 games is the worst start that the club has made to a Premier League season.
United striker Wayne Rooney has now scored 11 goals against Arsenal - more than any other Premier League player.
Crystal Palace 3-1 Liverpool
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Palace striker Dwight Gayle scored his fourth goal against Liverpool in just his third appearance against them.
As for Liverpool, they have been defeated in their last three Premier League matches.
One bright point for the Merseysiders was that Rickie Lambert scored his first goal for the club following his summer move from Southampton.
Hull City 1-2 Tottenham Hotspur
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The hosting Tigers have won just one of their last 11 Premier League fixtures.
Christian Eriksen marked his 50th appearance for Spurs by scoring the winning goal.
In all competitions, five of the last six matches involving Tottenham have finished in a 2-1 scoreline.
Aston Villa 1-1 Southampton
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When Gabriel Agbonlahor found the net for Villa, it was the first goal that Southampton had conceded in 439 minutes of Premier League action.
The draw means that Villa are without a win from their last eight outings.
Meanwhile, it was the lowest crowd (25,311 people) at Villa Park for a Premier League fixture in 15 years.
