Manchester United were held to a frustrating 1-1 draw at Southampton, while Tottenham beat Wolves 1-0 at Molineux on Nuno Espirito Santo's return.
Southampton collected their first point of the new season with a hard fought draw against Manchester United at St. Mary's.
Ralph Hasenhuttl's side took the lead after Che Adams' strike, that was deflected off Fred, beat David De Gea, and that goal came after a period of dominance from Manchester United, who created plenty of chances but failed to take any of them.
Mason Greenwood did eventually strike for Ole Gunnar Solskjaer's side to pull them level, but the Red Devils struggled to create after that.
The game finished level, but a draw for Manchester United did mean that they have now equalled Arsenal's Premier League record of 27 successive away games unbeaten. Their next away game is at Wolves next Sunday, where the have the chance to break the record.
It was a happy return to Molineux for Nuno Espirito Santo, as his new Tottenham team beat his old Wolves team 1-0 thanks to a ninth minute Dele Alli penalty.
The win was Spurs' second in successive games, with both coming through a 1-0 scoreline, while Wolves have now lost both of their openers under new coach Bruno Lage, both by a 1-0 scoreline also.
Adam Traore was electric throughout, but he was the man who squandered Wolves' best chance of the match in the 61st minute, with the Infogol model calculating he had a 55% chance of scoring his opportunity.
Wolves had a total of 25 shots in the game, but an xG total of just 1.69 meaning each shot had a 7% chance of being scored - in effect they were limited to low-probability attempts from range.
Lage's side now move onto a home game against Manchester United, while Spurs look to continue their 100% record in the Premier League with a home game against Watford.
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