As for Arsenal, the defending champions just needed one goal — a late one from their England international substitute Noni Madueke — to see off Nottingham Forest on Sunday.
On the day Manchester United ended a turbulent week by scrapping out a 1-1 draw at fierce rivals Leeds, it was a strike evoking memories of United star David Beckham's famous goal from the halfway line against Wimbledon 30 years ago that proved the day's highlight.
It was scored by Brighton's Paraguayan midfielder Diego Gomez, who boldly launched a shot from just inside Crystal Palace's half which flew over stranded Palace goalkeeper Walter Benitez into the net for an instant goal-of-the-season contender.
It was the second of three goals in the opening 10 minutes for Brighton, who swept to a 5-0 win over Palace and another statement victory in a campaign which has already seen the south-coast team overwhelm champions Arsenal 3-0.
As well as an own-goal, Brighton also scored through Yasin Ayari, Charalampos Kostoulas and Jack Hinshelwood at their Amex Stadium to move up to third.
Only three teams — Arsenal (2009-10), Man United (2011-12) and Manchester City (2019-20) — in the Premier League era have scored more after seven matches than their 23 goals.
Unlike Brighton, goals aren't proving so easy to come by for Arsenal, who have notched 11 from seven games.
Madueke proved the matchwinner after coming on as a halftime substitute, with the England winger cutting inside in the 80th minute and sending in a shot that deflected past Forest goalkeeper Matz Sels.
"We showed grit, determination — we showed a champion spirit here tonight," Madueke said.
Arsenal moved back into second, three points behind Manchester City.
Four days after his headline-grabbing outburst following a Champions League loss, Lisandro Martinez started for Man United at Elland Road but was substituted at halftime, with his team leading Leeds thanks to Bryan Mbeumo's 35th-minute strike.
Leeds equalised in the 51st through Dominic Calvert-Lewin, leaving Man United with just one win from their first seven league games this season — the fewest by this stage for the club in 40 years. They've had just two victories from 10 games in all competitions.
In the other match, Brazilian striker Evanilson scored one and set up the other for Marcus Tavernier in Bournemouth's 2-0 win over Sunderland, who were a man down from the 17th minute after a red card for defender Kevin Danso. It was Bournemouth's first league win of the season.
