Manchester City ensured that Liverpool’s lead at the top of the Premier League would stay at five points after running out 3-1 winners at Everton.
The Toffees gave the champions a real game particularly after Dominic Calvert-Lewin replied to Gabriel Jesus’ opener.
But second-half strikes from Riyad Mahrez and Raheem Sterling ensured the three points went to the visitors.
Earlier, Liverpool continued their perfect start to the league season after beating Sheffield United 1-0 at Bramall Lane.
The winning goal was scored by Georginio Wijnaldum, whose tame volley somehow managed slipped under Blades keeper Dean Henderson.
Tottenham and Chelsea both returned to winning ways in the Premier League with home wins over Southampton and Brighton respectively.
A chaotic first-half at the Tottenham Hotspur Stadium saw Spurs take the lead through Tanguy Ndombele before things suddenly took a turn for the worse.
Right-back Serge Aurier was sent off for a second bookable offence and a moment of madness from goalkeeper Hugo Lloris allowed Danny Ings to equalise for the visitors.
But Tottenham’s talisman Harry Kane was on hand to spare his team-mate’s blushes, and his 43rd-minute goal was enough to grind out a much-needed victory.
Chelsea boss Frank Lampard would’ve also been desperate for a win, having failed to claim three points from any of his opening three league games at home.
His side’s relentless pressure finally paid off when Mason Mount was brought down inside the box, with Jorginho converting the second-half penalty.
Willian then dispelled any nerves inside Stamford Bridge by doubling the lead after some fine work by substitute Callum Hudson-Odoi.
Elsewhere, Watford are now the only winless team in the Premier League after seven games, losing 2-0 to fellow strugglers Wolves at Molineux.
Matt Doherty and a Daryl Janmaat own goal sealed the win for Nuno Espirito Santo’s men.
And VAR stole the headlines once again, with controversy during the 2-2 draw between Bournemouth and West Ham, and in the clash between Aston Villa and Burnley, which ended with the same scoreline.
There was also a win for Crystal Palace, who beat Norwich 2-0 at Selhurst Park thanks to Luka Milivojevic’s penalty and Andros Townsend’s stoppage-time strike.
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Premier League results
Sheffield United 0-1 Liverpool
Aston Villa 2-2 Burnley
Bournemouth 2-2 West Ham
Chelsea 2-0 Brighton
Crystal Palace 2-0 Norwich
Tottenham 2-1 Southampton
Wolves 2-0 Watford
Everton 1-3 Manchester City