Manchester United remain without a Premier League win this season after being held 1-1 at Fulham on Sunday, while a Jack Grealish-inspired Everton opened their new stadium with a 2-0 victory over Brighton.
Ruben Amorim's United were left to rue Bruno Fernandes' wayward first-half penalty as they were pegged back at Craven Cottage.
Rodrigo Muniz's own-goal put United in front on the hour mark, but Emile Smith Rowe came off the bench to rescue a point for Fulham.
"After the (United) goal we were just thinking about the result. We were OK until the goal and then we were not smart in that moment," said Amorim.
The Portuguese coach is under pressure to show improvements after a disastrous 15th-placed finish last season, but so far his new £200 million ($270 million) forward line of Matheus Cunha, Bryan Mbeumo and Benjamin Sesko, who again started on the bench, is yet to fire.
Despite an encouraging performance, United lost 1-0 to title-chasing Arsenal in their season opener last weekend and will feel another two points slipped away in west London.
Fulham, though, felt the visitors got the better of two controversial calls.
United's penalty was awarded after a VAR review for grappling by Calvin Bassey on Mason Mount.
Fernandes is normally reliable from the spot, but blasted his effort high over the bar.
When United did finally get their first goal of the season it came via a Fulham body as Muniz deflected Leny Yoro's header into his own net.
However, the home side were furious that this time VAR did not intervene for a push by Yoro on Bassey.
Fulham still managed to rescue a point when former Arsenal midfielder Smith Rowe's run into the box was not tracked and he turned in Alex Iwobi's cross 17 minutes from time.
- Everton's new era -
After an emotional goodbye to Goodison Park, the club's home since 1892, Everton are hoping the move to a new 53,000 capacity stadium will rekindle their bygone glory days.
Only four clubs have won more English top-flight titles than Everton's nine.
However, they have not won a major trophy for 30 years and spent their final seasons at Goodison battling relegation.
"We're trying to find a way of moving the club on. I think this is a big step forward for Everton," said manager David Moyes.
Grealish has so far been the marquee new addition to Moyes' squad and showed glimpses of the talent that saw Manchester City pay Aston Villa £100 million for him four years ago, providing the assist for both goals.
Iliman Ndiaye scored the final goal at Goodison against Southampton in May and made more history with the first goal at Everton's new home.
Grealish was the creator with a drilled left-foot cross that Ndiaye timed his run perfectly to meet at the back post on 23 minutes.
Brighton should not have come away from Merseyside empty-handed but wasted a series of chances.
Kaoru Mitoma struck the bar and Jan Paul van Hecke's effort came back off the post, while Danny Welbeck spooned over with the goal gaping.
James Garner doubled Everton's lead early in the second period with a blistering strike from Grealish's lay-off.
Brighton still had the chance to set up a nervy finale, but Jordan Pickford saved Welbeck's poor penalty to round off a memorable afternoon for the Toffees.
- Nuno no go -
Nottingham Forest manager Nuno Espirito Santo insisted he wants to remain in charge after his side's 1-1 draw at Crystal Palace.
Callum Hudson-Odoi rescued a point for Forest after Ismaila Sarr's first-half opener for Palace.
Nuno said on Friday his relationship with owner Evangelos Marinakis had deteriorated as odds on him being the first Premier League manager of the season to be sacked were slashed.
"That is nonsense. That does not make any kind of sense," said the Portuguese coach on whether he is trying to engineer an exit from the club.
K.Cox--LCdB