Arsenal's win was set up by an early goal from Ezri Konsa, who bundled the ball home from close range in the seventh minute after Martin Odegaard's corner caused chaos in the Everton box. Konsa said: "I've come to this stadium for many seasons; I know how tough it is to play against us. We are champions and to be champions you've got to win games consistently."
Ben White and Gabriel, each making their 200th appearance for the club, combined for the second goal in the 68th minute. White clipped a cross to the far post, where Gabriel headed home to give Arsenal a two-goal cushion. The result moved Mikel Arteta's side to 21 points, level with Manchester City after eight games.
Earlier, at Villa Park, Aston Villa climbed to sixth place with their third successive league win over City. Nicolas Jackson opened the scoring in the sixth minute after Marc Guehi's heavy touch allowed John McGinn to set up the striker. Erling Haaland equalised soon after half-time, but Jackson struck the winner on the hour when Ibrahim Mbaye cut the ball back for his Senegal international teammate, whose shot sneaked under the diving keeper Gianluigi Donnarumma.
"It was incredible; we got the win, which is the most important thing. Man City are a strong team, the league leaders," Jackson told TNT Sports. "It's just the beginning; we're trying to work game by game."
City are playing under the shadow of an independent commission's findings that they committed 114 breaches of Premier League financial rules. City have denied wrongdoing and appealed.
At Stamford Bridge, Spurs took the lead in the 77th minute when Chelsea goalkeeper Mike Penders punched a corner into his own net in his first league start. Chelsea were reduced to 10 men when Cole Palmer was shown a second yellow card in the 80th minute for a late challenge on Conor Gallagher. Mathys Tel sealed the victory in the 87th minute with a surging run and low shot from outside the box.
"It's very special, because we came here a lot of times and didn't get a win," said Tel. "And today, we made it together, all together, we showed great mentality, and I'm very happy about it."
Spurs climbed to 12th with the win, and Fulham beat Coventry City 1-0 to move to 13th, while Coventry slipped to 19th.