Philippe Coutinho's goal, which opened the scoring at Goodison Park, was the first that Everton goalkeeper Tim Howard had conceded in five hours and 34 minutes.
It was also the first time that the Brazilian had scored from his 20 shots - more than any other player without finding the net.
No player has scored more goals with his head than Daniel Sturridge, who has three so far.
Arsenal 2-0 Southampton
Olivier Giroud has scored the first goal in five Premier League encounters this term, a figure that no other player can match.
The Frenchman's brace also meant that he has scored from half of his 14 shots on target.
The Saints are still looking for their first victory at Arsenal in the Premier League era, having not returned from North London with all three points since 1987.
Fulham 1-2 Swansea City
Only Sunderland (three) can beat Fulham's record of two own goals this season after Aaron Hughes put through his own net.
Staying with own goals, the visiting Swans have now benefited from three this term.
Meanwhile, Scott Parker's strike for Fulham was the first that he has scored in the Premier League since he found the net for West Ham United at Liverpool back in February 2011.
Hull City 0-1 Crystal Palace
Hull were previously unbeaten at the KC Stadium, having picked up 11 points from a possible 15.
In contrast, visiting Palace had not collected a single point on the road prior to their victory.
Barry Bannan's first goal for the club was just the second of his career. The first he scored back in September 2011 for Aston Villa against Queens Park Rangers.
Newcastle United 2-1 Norwich City
Loic Remy continued his recent positive form by scoring his eighth goal in 10 outings for the Magpies.
What's more, his teammate and fellow Frenchman, Yoann Gouffran, has now either scored or assisted in each of his least three Premier League matches.
The Canaries have won just three matches away from home under the management of Chris Hughton.
Stoke City 2-0 Sunderland
Yet another red card for Sunderland - their seventh of 2013, which is more than any other Premier League club has received.
The victory was the 100th of Mark Hughes's career as a manager of a top-flight club, having also taken charge of Blackburn Rovers, Manchester City and Queens Park Rangers.
Staying with Stoke, Glen Whelan had a 100% success rate with his 63 passes.
West Ham United 0-3 Chelsea
Chelsea midfielder Frank Lampard ended a run of 10 Premier League encounters without a goal by scoring a brace.
The England international has now also scored five goals in as many outings against his former team.
Up the other end, the hosting Hammers did not record their first shot on target until the third minute of second-half stoppage time.
Manchester 6-0 Tottenham Hotspur
The Citizens have fired in more goals at home (26) than any of their rivals so far this campaign.
Sergio Aguero's brace took his season's tally to 10, which is more than Tottenham (nine) have managed to score as a team.
Visiting Spurs had not lost a fixture by five or more goals since a 6-1 defeat against Chelsea in December 1997.
Cardiff City 2-2 Manchester United
When Wayne Rooney opened the scoring at the Cardiff City Stadium, he became the first Premier League player to bag 50 goals on a Sunday.
His teammate, Ryan Giggs, has now featured against 45 of the 46 teams to have played in the top flight - the other being United.
Cardiff frontman Fraizer Campbell has now scored twice against his former club.
West Bromwich Albion 2-2 Aston Villa
West Brom centre-forward Shane Long had never previously scored two goals in one Premier League fixture.
The Republic of Ireland international's second of the night was the 300th Premier League goal of the season.
The fightback from Villa means that they have recovered seven points from losing positions, which is more than any other team have managed.
