Tottenham Hotspur 0-0 Liverpool
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No solo manager has won his first match in charge of Liverpool during the Premier League era.
The draw brought an end to Liverpool's five-match winning streak against the North Londoners, during which time they scored 18 goals.
Tottenham's current unbeaten run of eight games is the longest of all the sides in the top flight.
Chelsea 2-0 Aston Villa
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Struggling Villa have not won away at Chelsea since Stephen Ireland was on target in a 3-1 victory back in December 2011.
Also, they have not kept a Premier League clean sheet at Stamford Bridge since March 1998.
Diego Costa scored his second Premier League goal of the season in what was his seventh appearance. After the same number of games last term, the Spaniard had found the net nine times.
Crystal Palace 1-3 West Ham United
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Palace's goalscorer Yohan Cabaye has scored a penalty in each of his last three appearances.
Of the 12 defeats that Palace have suffered under Alan Pardew's management, eight have come at Selhurst Park.
The Hammers have now won four matches away from home, one more than they managed over the whole of last term.
Everton 0-3 Manchester United
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Man United captain Wayne Rooney scored an away goal in the Premier League for the first time since November 2014.
Also on the scoresheet was Ander Herrera, who has scored eight Premier League goals from just 10 shots on target.
Everton's Gareth Barry started in a Premier League game for the 550th time - only David James (571) has started more.
Manchester City 5-1 Bournemouth
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In his last six games for Man City, summer signing Kevin De Bruyne has scored four goals and assisted another four.
Another new addition - Raheem Sterling - became the 11th player under the age of 21 to score a hat-trick in the Premier League.
Defeated Bournemouth scored through Glenn Murray with what was their only shot on target.
Southampton 2-2 Leicester City
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Leading goalscorer Jamie Vardy has scored 10 goals in his last 10 Premier League appearances.
His two-goal contribution ensured that Leicester are now unbeaten in their last eight away matches.
Nine of the 12 goals that Southampton have conceded this season have been shipped at the St Mary's Stadium.
West Bromwich Albion 1-0 Sunderland
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Of Saido Berahino's last 17 goals for the Baggies, 13 have been scored at The Hawthorns.
However, West Brom are still the only team in the Premier League to have not scored in the opening 30 minutes of a game this season.
Bottom-of-the-table Sunderland have conceded 19 goals from their nine outings.
Watford 0-3 Arsenal
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Watford have still never won a Premier League encounter in the month of October, drawing four times and losing on six occasions.
The Hornets have lost all five of their most recent meetings with the Gunners - a run that dates back to April 1988.
Arsenal's Chile international Alexis Sanchez has now scored 10 goals in his last six appearances for club and country.
Newcastle United 6-2 Norwich City
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The hosting Magpies scored six goals in a Premier League game for the first time since August 2010.
Georginio Wijnaldum became just the second Newcastle player after Alan Shearer to score four or more goals in one Premier League match.
Norwich have now conceded 20 goals this season, which is more than any of their counterparts.
Swansea City 0-1 Stoke City
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The visiting Potters have won consecutive Premier League away games for only the second time.
The clean sheet was just the third that Stoke had kept in their last 19 league visits to Swansea.
Meanwhile, the hosting Swans have now won only two of their last 11 Premier League games.
