Everton 3-1 Chelsea
Steven Naismith's perfect hat-trick saw the Scot become the sixth Premier League player to have scored three goals in one match after coming on as a substitute.
What's more, he is the fifth player to hit a treble against Chelsea in the Premier League and the first since 2011.
As for champions Chelsea, they have made their worst start to a new season since the 1986-87 campaign.
Arsenal 2-0 Stoke City
Arsenal frontman Olivier Giroud found the net in the Premier League for just the second time in 12 outings.
Meanwhile, Arsenal's other goalscorer - Theo Walcott - extended his record of having found the net in nine consecutive campaigns.
The scoreline would have been even greater but for Stoke's Jack Butland, who made 10 saves at the Emirates Stadium - no goalkeeper has made more stops in one appearance this term.
Crystal Palace 0-1 Manchester City
This encounter marked Man City's fifth straight victory on the road - the first time they have achieved that feat since 1912.
Match-winner Kelechi Iheanacho is the third youngest goalscorer to find the net for the Citizens in the Premier League after Micah Richards and Daniel Sturridge.
Of the 40 points that Palace have collected under Alan Pardew's management, only 16 of them have been earned at Selhurst Park.
Norwich City 3-1 Bournemouth
The victory was Norwich's first over Bournemouth at Carrow since 1951, having lost five and drawn four of the previous nine meetings in Norfolk.
Debutant Matt Jarvis scored in the Premier League for the first time since April 2014 - a run that dated back 18 appearances.
Seven of the nine goals that Bournemouth have conceded this season have come away from home.
Watford 1-0 Swansea City
Visiting Swansea have now kept only one clean sheet in their last seven Premier League away encounters.
Watford centre-forward Odion Iglaho has now scored 18 league goals in 2015 - more than any other player in England's top four divisions.
His goal was the 100th to have been scored in the Premier League at Vicarage Road and the first since 2007.
West Bromwich Albion 0-0 Southampton
The hosting Baggies have kept 13 clean sheets since Tony Pulis took charge at The Hawthorns in January 2015 - no Premier League team has recorded more shutouts during that time.
As for Southampton, they are now without a victory from their last 10 away encounters in the Premier League.
Ronald Koeman's men have also failed to find the net in four of their last six outings.
Manchester United 3-1 Liverpool
Deadline-day signing Anthony Martial, who cost United a reported £36m, scored with his first ever shot at goal in the Premier League.
The French youngster's effort helped the Red Devils to secure their fourth victory in the previous five encounters against their arch rivals.
Liverpool centre-forward Christian Benteke has scored in his last three appearances against United, with his previous two goals having come in Villa colours.
Sunderland 0-1 Tottenham Hotspur
England midfielder Ryan Mason scored what was only his third goal for Tottenham in his 46th appearance for the North London club.
The victory extended Tottenham's unbeaten run against the Black Cats to 11 matches, eight of which they have won.
Meanwhile, Dick Advocaat's Sunderland have now gone eight Premier League games without a victory, drawing four and losing four.
Leicester City 3-2 Aston Villa
The Foxes have played host to Villa in the Premier League 10 times and have tasted defeat on only one occasion.
The three goals took Leicester's tally for the season to 11, which is a joint division-high with league leaders Man City.
Tim Sherwood's Villa have kept just one clean sheet in their last nine outings in all competitions.
West Ham United 2-0 Newcastle United
The travelling Magpies have now won just one of their last 16 Premier League away encounters.
The defeat also extended Newcastle's winless run at Upton Park to four matches, with their last victory in East London having come back in October 2010.
West Ham's Dimitri Payet, who scored both of his side's goals, took his Premier League tally for the campaign to three.
