As the Premier League returned with a bang after the international break, Liverpool were rocked by Brighton forward Leandro Trossard's hat-trick in a 3-3 draw at Anfield.
But it was Arsenal who stole the spotlight as Mikel Arteta's side made it seven wins from eight league games, moving them four points clear at the top of the table.
Thomas Partey put Arsenal ahead early in the first half of the north London derby at the Emirates Stadium.
Harry Kane equalised with a penalty but third-placed Tottenham imploded after the interval as Hugo Lloris's mistake allowed Gabriel Jesus to restore Arsenal's lead.
Tottenham defender Emerson Royal was sent off for an ugly foul on Gabriel Martinelli before Granit Xhaka's goal ensured Arsenal would avenge the 3-0 defeat against their hated neighbours last season that cost them a Champions League place.
Ending Tottenham's 13-match unbeaten run in the league was a significant statement of intent from Arsenal.
"They were phenomenal. We went from it and we created great energy in the stadium and deserved to win the game," Arteta said.
"We were free, courageous and brave. This is what we demand from the players."
At Selhurst Park, Chelsea left it late to give Potter his first win in his second match since arriving from Brighton to replace the sacked Thomas Tuchel.
Chelsea, who drew 1-1 with RB Salzburg in the Champions League in Potter's first game, suffered a nightmare start on seven minutes as Wesley Fofana squandered possession and Jordan Ayew fed Odsonne Edouard to fire into the top corner.
Chelsea defender Thiago Silva escaped a red card when he was only booked for stopping Ayew's attack by deliberately handling.
Gallagher strikes late
Silva made the most of that escape as he provided the assist for Pierre-Emerick Aubameyang's 38th minute equaliser.
The Brazilian headed the ball towards Aubameyang and he let it bounce across his body before swivelling to fire a half-volley into the bottom corner from just inside the area.
It was Aubameyang's first Chelsea goal since signing from Barcelona on transfer deadline day.
Conor Gallagher, who spent last season on loan at Palace, won it for Chelsea in stoppage-time when the substitute curled a fine finish into the top corner.
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Potter's replacement at Brighton, former Shakhtar Donetsk boss Roberto De Zerbi, enjoyed a memorable introduction to the Premier League.
Trossard fired Brighton ahead inside four minutes after punishing sloppy Liverpool defending.
With Liverpool in disarray, the Belgian forward struck again in the 18th minute.
Roberto Firmino gave Liverpool a 33rd minute lifeline when he turned in Mohamed Salah's flick.
And Firmino grabbed Liverpool's leveller with a 54th minute equaliser as the Brazilian side-stepped his marker to convert Luis Diaz's pass.
Jurgen Klopp's men looked to have completed an epic comeback in the 63rd minute when Albion keeper Robert Sanchez punched a corner that hit Adam Webster and deflected into his own net.
But Trossard sealed his treble with a close-range finish from Kaoru Mitoma's cross to silence Anfield with seven minutes left.
Newcastle ended their six-match winless run in the league as Eddie Howe's men swept to a 4-1 rout of 10-man Fulham at Craven Cottage.
Fulham's Nathaniel Chalobah was sent off after eight minutes for a reckless lunge on Sean Longstaff.
Callum Wilson volleyed home after 11 minutes before Miguel Almiron fired into the top corner in the 33rd minute.
Longstaff bagged the third goal three minutes before half-time and Almiron struck again in the 57th minute.
Bobby De Cordova-Reid's 88th minute goal was no consolation for Fulham.
Everton won 2-1 at Southampton as Conor Coady and Dwight McNeil both scored their first goals for the club after Joe Aribo put the hosts in front.
Bournemouth and Brentford shared a goalless draw at Dean Court.
