Jack Grealish was among the scorers as champions Manchester City eased past Norwich City 5-0 for their first win of the season but it was Liverpool and Brighton who were setting the pace at the top of the Premier League as they both maintained their 100 percent records.
Liverpool enjoyed returning to a packed Anfield with their easy 2-0 win over Burnley in Saturday's lunchtime fixture, while Brighton also earned a 2-0 home win over Watford to move onto six points.
Man City had fallen to a 1-0 defeat at Tottenham in their opening game but had no trouble in seeing off the newly-promoted Canaries at the Etihad Stadium with British record signing Grealish scoring in an unconventional manner, the ball bouncing off his knee into the net 22 minutes into his home debut.
His goal had come after keeper Tim Krul's unfortunate own goal had given the hosts an early lead.
Aymeric Laporte then added to the scoring in the second half and substitutes Raheem Sterling and Riyad Mahrez piled the misery on Norwich, who slipped to a second successive defeat on their return to the top tier.
Diogo Jota and Sadio Mane were on target for Liverpool as Anfield's first full house in 17 months left manager Jurgen Klopp saying that the return of such a great atmosphere made him feel like a dream had come true.
In the late game at Brighton, first-half goals from Shane Duffy and Neal Maupay saw off newly-promoted Watford.
Elsewhere, Leeds United winger Raphinha blasted in a second-half equaliser as the battling Yorkshire side came back twice to secure a 2-2 draw with Everton.
Raphinha, who was called up to the Brazilian squad for the first time last week, lashed one past goalkeeper Jordan Pickford in the 72nd minute after Everton winger Demarai Gray thought he had sealed a second straight win for the visitors.
Everton had gone up 1-0 against the run of play through Dominic Calvert-Lewin's 30th-minute penalty, following a VAR check after the on-field official did not spot Leeds skipper Liam Cooper's tug on the striker's shirt.
The home fans, though, found their voice when Mateusz Klich ran on to Patrick Bamford's fine pass to equalise before the break.
At Villa Park, Aston Villa's new signing Danny Ings scored with a stunning bicycle kick in first-half stoppage time to help them beat Newcastle 2-0, with Anwar El Ghazi also converting a second-half penalty.
Crystal Palace were held to a goalless home draw by promoted Brentford in a game short on quality, leaving Patrick Vieira's Palace still waiting for a goal under their new manager.
Australian Associated Press