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John Terry's opening goal at Stamford Bridge marked the first time in eight seasons that the Chelsea skipper had scored in consecutive games.
His goal helped the Blues stay three points clear of Manchester City at the top of the Premier League table. The team which has held this position on Boxing Day has won the title in eight out of the last 10 seasons.
This was only the third game this term in which West Ham failed to score, and their first on the road.
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Raheem Sterling scored his first Premier League goal since September to secure Liverpool all three points at Turf Moor.
It was the first time since October that newly-promoted Burnley had lost a top-flight match on home soil.
Sam Vokes's appearance off the bench was his first in nine months following a knee ligament injury. The Welsh striker scored 20 Championship goals last season.
Crystal Palace 1-3 Southampton
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Strikes from Ryan Bertrand and Toby Alderweireld mean that Southampton now have six Premier League goals from defenders this season - more than any other side.
Palace's senior strike force - Fraizer Campbell, Dwight Gayle, Marouane Chamakh and Kevin Doyle - have scored only one goal between them in the club's last 11 Premier League matches.
The result saw the Saints climb back into the top four of the table and consigned Palace to the drop zone.
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Bojan's penalty inflicted on Everton a third home loss of the season - the same number that they suffered during the entirety of last campaign.
The victory was the fourth time this term that Stoke have beaten one of last season's Premier League top six.
The win took them above the Toffees, who have won just one of their last six league games, and to 11th in the table.
Leicester City 1-2 Tottenham Hotspur
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Tottenham's last six Premier League victories have all come by a 2-1 scoreline. Harry Kane (five) and Christian Eriksen (four) have scored nine of these 12 goals between them.
This result marked the first time since February 2013 that Spurs have recorded three successive top-flight wins.
Meanwhile, Leicester have lost 10 of their last 11 Premier League matches and remain rooted to the bottom of the table, a Boxing Day position from which only two teams have survived relegation.
Manchester United 3-1 Newcastle United
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Wayne Rooney's brace at Old Trafford took him to 180 Premier League goals and within seven of second-place Andy Cole - formerly of both the Red Devils and Newcastle - in the all-time scoring charts.
United have now won 20 of their 23 Premier League matches on Boxing Day - more than any other side.
At 17 years and 319 days, Adam Armstrong became Newcastle's youngest ever Premier League starter.
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Hull's victory at the Stadium of Light ended a 10-match winless Premier League run and lifted them out of the relegation zone.
Adam Johnson's opening goal after 30 seconds was the second time that he had scored in five Premier League minutes following his late winner at Newcastle United.
Gaston Ramirez's equaliser was his first Premier League goal in over a year and his first since joining the Tigers on loan from Southampton.
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Swansea won on December 26 for the first time in seven years against an Aston Villa side who have the worst Boxing Day record in Premier League history - having won only three of 23 matches.
Villa have the third lowest average possession (43.5%) in the Premier League, but have had more of the ball than their opponents in their last four away games - 57% at the Liberty Stadium.
Swansea have won three Premier League matches by a 1-0 scoreline this campaign - as many as any other side.
West Bromwich Albion 1-3 Manchester City
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Man City have won their last seven Premier League matches - a feat that they have managed twice before during Manuel Pellegrini's 18-month reign.
The Citizens have found the net six times in two games without fielding a recognised striker - with Yaya Toure and David Silva contributing four of them.
Both City midfielder Fernando and Baggies striker Brown Ideye scored their first Premier League goals since their summer arrivals.
Arsenal 2-1 Queens Park Rangers
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Alexis Sanchez has now scored or assisted in 12 of his 17 Premier League appearances since joining Arsenal from Barcelona for £32m in the summer.
The Chilean's penalty miss at the Emirates Stadium was the first spot kick saved by Queens Park Rangers goalkeeper Robert Green in over four years.
Green's exploits were not enough to prevent the Hoops from falling to their eight successive away defeat from the start of the season - the first time that has happened since Bolton Wanderers in 1996-97.
Joe Fish
