Liverpool beat Sheffield United 1-0 on Saturday to maintain their place at the top of the Premier League and make it seven wins out of seven for Jurgen Klopp's men.
Defending champions Manchester City remain five points behind the Reds in second place after beating Everton 3-1 at Goodison Park.
Elsewhere, Chelsea picked up their first home Premier League win of the season with a 2-0 win over Brighton & Hove Albion, while Tottenham Hotspur returned to winning ways with victory at home to Southampton.
Saturday also saw wins for Crystal Palace and Wolverhampton Wanderers, while Aston Villa were held by Burnley, and Bournemouth drew 2-2 at home to West Ham United.
Sheffield United 0-1 Liverpool
Aston Villa 2-2 Burnley
Bournemouth 2-2 West Ham United
Chelsea 2-0 Brighton
Crystal Palace 2-0 Norwich City
Tottenham 2-1 Southampton
Wolverhampton Wanderers 2-0 Watford
Everton 1-3 Manchester City
Standings (Played, Won, Goal Difference and Points)
1. Liverpool: 7, 7, +13, 21
2. Manchester City: 7, 5, +20, 16
3. West Ham United: 7, 3, 1, 12
4. Tottenham Hotspur: 7, 3, +5, 11
5. Leicester City: 6, 3, +3, 11
6. Chelsea: 7, 3, +1, 11
7. Bournemouth: 7, 3, +1, 11
8. Arsenal: 6, 3, +1, 11
9. Crystal Palace: 7, 3, -1, 11
10. Burnley: 7, 2, +1, 9
11. Manchester United: 6, 2, +2, 8
12. Sheffield United: 7, 2, 0, 8
13. Wolverhampton Wanderers: 7, 1, -2, 7
14. Southampton: 7, 2, -4, 7
15. Everton: 7, 2, -6, 7
16. Brighton and Hove Albion: 7, 1, -5, 6
17. Norwich City: 7, 2, -7, 6
18. Aston Villa: 7, 1, -3, 5
19. Newcastle United: 6, 1, -4, 5
20. Watford: 7, 0, -16, 2
Liverpool remain the only team in the top flight with a 100 per cent record, although they needed a slice of luck to pick up their seventh win of the season against Sheffield United at Bramall Lane.
Goalkeeper Dean Henderson ought to have saved Georginio Wijnaldum's shot but allowed it to squirm through his grasp and into the back of the net for the only goal of the game.
The Reds were not at their best but did have other chances to score. Sadio Mane sliced horribly wide when clean through and struck a post shortly before half-time.
Liverpool have been on a relentless run of form in the top flight, as highlighted by Football on BT Sport:
Their record of seven straight wins at the start of the season is also a run bettered only by one other club, per Opta:
7 - Liverpool have won each of their opening seven league games to a season for only the second time in the club's history (won first eight in 1990-91), and are only the second team to do so in the @premierleague after Chelsea in 2005-06 (won first nine). Super. https://t.co/ZJyd1P5dYQ
Liverpool will hope they can at least match Chelsea's record, but they face some tricky fixtures ahead. Leicester City are up next at Anfield before a trip to Manchester United and a visit from Spurs.
Losers: Premier League goalkeepers
Henderson's error against Liverpool proved to be the game's defining moment, though it was a rare mistake from the 22-year-old Manchester United loanee:
Yet Henderson was not the only top-flight goalkeeper who endured a bad day. Tottenham's Hugo Lloris was also at fault for gifting Southampton an equaliser in a 2-1 win for Spurs:
TV presenter Gary Lineker offered his view on the Frenchman's error:
Watford stopper Ben Foster also had a tough afternoon at Molineux. The former West Bromwich Albion man conceded twice and was targeted by Wolves fans, according to sports journalist Luke Hatfield:
Norwich also endured problems in their defeat to Palace. Schalke loanee Ralf Fahrmann came in for the injured Tim Krul and was forced off after 22 minutes, meaning the Canaries had to turn to third-choice goalkeeper Michael McGovern.
Winner: Gabriel Jesus
Manchester City striker Gabriel Jesus spoke of his frustration at a lack of game time with the Premier League champions ahead of Saturday's match against Everton.
The Brazilian told Esporte Interativo (h/t Goal's Josh Thomas): "I'm over the 'I have to wait' phase. I've been here for almost three years, it's my fourth season, and that makes me want to play more."
Manager Pep Guardiola put Jesus in from the start at Goodison Park, and he was rewarded with a goal after just 24 minutes.
Opta highlighted just how effective Jesus is as a starter for club and country:
The goal will help strengthen Jesus' push for a starting spot at the Etihad Stadium. Sergio Aguero remains first choice, but a total of six games in October may afford Jesus some more opportunities.
Loser: Serge Aurier
Tottenham picked up their third win of the season on Saturday but had to do it the hard way after Serge Aurier was sent off on 31 minutes.
Mauricio Pochettino's men were leading 1-0 when Aurier was booked twice in the space of four minutes and given his marching orders by referee Graham Scott.
His first booking came for a poor challenge on Sofiane Boufal, and he was then carded again for a needless foul on Ryan Bertrand that left the referee with little choice but to brandish a red card.
Rob Draper at the Mail on Sunday offered his view on Aurier's bookings:
Spurs showed great character to win the game 2-1 despite playing for an hour with 10 men, with Southampton unable to capitalise on Aurier's first-half dismissal.
Winner: Frank Lampard
Frank Lampard saw his Chelsea side beat Brighton 2-0 at Stamford Bridge to secure the Blues' first home Premier League win under their new manager and their first clean sheet of the season:
Goals from Jorginho and Willian were enough to secure all three points and send Lampard's men into sixth place in the table.
Lampard offered his thoughts on his team's performance after the match:
The result means Chelsea have bounced back well from Sunday's 2-1 defeat to Liverpool. They thrashed Grimsby Town 7-1 in the Carabao Cup in midweek, and victory over Brighton sets them up nicely for Wednesday's trip to Lille in the Champions League.
Losers: Watford's defence
Watford remain bottom of the Premier League without a win after seven games following Saturday's 2-0 defeat to Wolves.
The Hornets are the only team in the top flight not to have won this season, and they have the worst defensive record in the top flight with 20 goals conceded in seven outings.
The re-appointment of Quique Sanchez Flores has done little to stem the flow of goals conceded. Watford have let in 13 goals in the four matches he has overseen in his second spell with the club.
Flores spoke about his side's defending after the game, per Simon Stone at BBC Sport:
Watford are already three points adrift at the bottom after seven games and must tighten up defensively if they are to remain in the Premier League.