Liverpool maintained their stunning start to the season – and eight-point lead at the summit – with a 2-1 win over Crystal Palace at Selhurst Park.
Jose Mourinho wasted little time in making his mark at Tottenham after he was brought in to replace Mauricio Pochettino, guiding the north London club to a 3-2 win over sorry rivals West Ham.
Manchester City, meanwhile, bounced back from their damaging 3-1 defeat to Liverpool before the international break with an entertaining 2-1 victory against Chelsea – a result which saw them leapfrog Frank Lampard's side into third.
The game of the weekend came on Sunday when Sheffield United and Manchester United played out a thrilling 3-3 draw at Bramall Lane, with the visitors coming from two goals down to lead 3-2 before Oli McBurnie's late equaliser.
Here, we look at the best milestones and stats from another action-packed weekend of Premier League action.
RELENTLESS REDS MARCH ON AGAINST PALACE
Liverpool became only the fourth side in English top-flight history to have as many as 37 points from their opening 13 league games to a season after their slender win at Selhurst Park.
Sadio Mane opened the scoring shortly after half-time, which was perhaps unsurprising given his superb record against the Eagles. His deflected strike means he has now scored eight Premier League goals against Palace – more than against any other opponent.
It had looked like Jurgen Klopp's Liverpool would drop points for just the second time this season when Wilfried Zaha levelled with eight minutes remaining. That was the Ivorian's first goal in 14 Premier League games, ending a run of 1245 minutes without scoring.
Roberto Firmino had the final say, though, prodding home after a corner had caused chaos in the Palace penalty area. Since the start of last season, Liverpool have scored 38 goals from set-pieces in the Premier League (including penalties) – eight more than any other club.
The win takes the Reds' unbeaten run in the Premier League to 30 matches. Only Arsenal (49 games in October 2004) and Chelsea (40 in October 2005) have ever had longer runs without defeat in the history of the competition.
MOURINHO BACK WITH A BANG
Mourinho made a triumphant return to management as Tottenham saw off West Ham at the London Stadium.
Having lost his first ever competitive game as manager, with Benfica in September 2000, Mourinho has gone unbeaten in his first game in charge at each of his eight clubs since then.
The former Manchester United and Real Madrid boss was indebted to star duo Harry Kane and Son Heung-min, who scored other side of Lucas Moura's close-range effort.
Kane has now scored eight goals in his last nine Premier League games against the Hammers, while Son's strike means he is Spurs' leading scorer in all competitions in 2019 with 19 – one more than Kane.
GUARDIOLA SETS UNWANTED RECORD IN CITY WIN
City claimed a valuable Premier League victory over Chelsea on Saturday, despite recording the lowest share of possession any Pep Guardiola side has managed in a top-flight game.
City's possession figure of just 46.74 per cent is the lowest any team coached by Guardiola has registered in 381 top-flight matches.
N'Golo Kante gave Chelsea a 21st-minute lead but, remarkably, Lampard's side did not manage another shot on target for the remainder of the match.
City stormed back after that early setback to claim all three points thanks to goals from Kevin De Bruyne and Riyad Mahrez. The Algerian has now been directly involved in 10 goals in his 11 starts across all competitions this season, scoring four and creating six more.
BRAMALL LANE DRAMA LEAVES SOLSKJAER WITH MIXED EMOTIONS
Ole Gunnar Solskjaer gave his Manchester United players credit after they scored three goals in seven minutes to overturn a two-goal deficit against Sheffield United but condemned their display for the first hour at Bramall Lane.
Goals from John Fleck and Lys Mousset put the Blades in front and United have not kept a clean sheet on the road in the Premier League in their last 12 matches - their worst top-flight run since going 15 away games without a shutout between September 1985 and April 1986.
Fortunately for Solskjaer, his young charges rallied and Brandon Williams and Mason Greenwood struck in quick succession to make it 2-2. The last time two teenagers scored in a Premier League game for United was in October 2005, when Wayne Rooney and Giuseppe Rossi netted against Sunderland.
Marcus Rashford's goal in the 79th minute put United on course for a win that did not transpire, but the England forward continued his good record against newly-promoted opponents - he has been involved in eight goals in his last five Premier League appearances against newcomers (four goals, four assists).