Liverpool were held to a 1-1 draw with Newcastle United on Sunday after Joselu cancelled out Philippe Coutinho's opener at St James' Park.
Meanwhile, Arsenal moved level on points with Chelsea after beating Brighton & Hove Albion 2-0 at the Emirates Stadium, thanks to goals from Nacho Monreal and Alex Iwobi.
Sunday's other fixture saw yet another defeat for Everton, who were beaten 1-0 at Goodison Park by Burnley.
The defeat is the Toffees' fourth in their last five Premier League outings, while Burnley continue their impressive start to the season by moving into sixth place in the table.
Read on for a breakdown of the latest Premier League results and standings as well as an updated list of this season's current top scorers:
Sunday's Premier League Results
Arsenal 2-0 Brighton & Hove Albion
Everton 0-1 Burnley
Newcastle United 1-1 Liverpool
Visit the official Premier League website for a breakdown of the latest results.
Premier League Top 10 Scorers (Goals)
1. Romelu Lukaku, Manchester United (7)
2. Sergio Aguero, Manchester City (6)
3. Harry Kane, Tottenham Hotspur (6)
4. Alvaro Morata, Chelsea (6)
5. Raheem Sterling, Manchester City (5)
6. Jamie Vardy, Leicester City (5)
7. Gabriel Jesus, Manchester City (4)
8. Alexandre Lacazette, Arsenal (4)
9. Mohamed Salah, Liverpool (4)
10. Richarlison, Watford (3)
Via the Premier League's official website
Premier League Standings (Goal Difference)
1. Manchester City 19 (20)
2. Manchester United 19 (19)
3. Tottenham Hotspur 14 (9)
4. Chelsea 13 (6)
5. Arsenal 13 (13)
6. Burnley 12 (12)
7. Liverpool 12 (1)
8. Watford 12 (-1)
9. Newcastle United 10 (1)
10. West Bromwich Albion 9 (-2)
11. Huddersfield Town 9 (-2)
12. Southampton 8 (-2)
13. Stoke City 8 (-4)
14. Brighton & Hove Albion 7 (-4)
15. West Ham United 7 (-6)
16. Everton 7 (-8)
17. Leicester City 5 (-3)
18. Swansea City 5 (-5)
19. Bournemouth 4 (-7)
20. Crystal Palace 0 (-17)
Visit the official Premier League website for the latest results and a look at the standings in full.
Liverpool frustrated by Newcastle
Liverpool started off well against Newcastle and went ahead through Phillipe Coutinho's curling strike that gave goalkeeper Rob Elliot no chance at all.
Opta noted how the Brazilian's long-range shooting is unrivalled in the Premier League:
However, the hosts were quick to respond, with Joselu exploiting plenty of space in the Liverpool backline and racing through on goal.
While Joel Matip did well to get back and make a recovery tackle, the ball took a touch off the striker and beat goalkeeper Simon Mignolet.
Liverpool pressed for a winner but struggled to break down a disciplined and determined home side who fought hard for their point.
Goal's Melissa Reddy noted how Liverpool have struggled for form since the last international break:
Jurgen Klopp's side may therefore welcome the break from Premier League football, particularly with their next fixture being a visit from rivals Manchester United.
Arsenal continue winning ways
Arsenal's good run of form continued with a victory against Brighton, with the Gunners picking up a fourth consecutive Premier League clean sheet.
Nacho Monreal opened the scoring for the hosts, firing home from inside the penalty area after Brighton had failed to clear a free kick.
It was a fine finish from the full-back, and his performance drew praise from Goal's Chris Wheatley:
Arsenal added a second after the break from a flowing passing move that culminated in Alex Iwobi smashing past goalkeeper Mat Ryan, following a clever backheel from Alexis Sanchez.
Opta highlighted just how crucial the Chilean is to Arsenal:
The victory means Arsenal remain unbeaten since the August defeats to Stoke City and Liverpool, and the club may be disappointed to see their fun of form halted by the international break.
The Gunners have won six of their last seven games, which leaves them six points off the top of the table after having already played both Chelsea and Liverpool away from home.