Jose Mourinho endured his first Premier League loss since returning to Chelsea at Everton on Saturday, while Manchester City were frustrated in a draw at Stoke City.
However, for Arsenal and Tottenham Hotspur there were routine victories as the league swung back into action for the first time since the transfer window closed before the international break.
Samuel Eto’o failed to make an immediate scoring impact on his Chelsea debut as Steven Naismith gave Everton a 1-0 win.
Naismith headed into the Chelsea net from close range in first-half stoppage-time on his 27th birthday after Nikica Jelavic nodded the ball across to the forward.
While it was Roberto Martinez’s first win as Everton manager after three draws, Chelsea have two wins from four league matches since Mourinho — the self-styled “Special One” — returned after six years.
“It was a special game, a special opposition and a very good performance,” Martinez said.
Mourinho saw things differently.
“We didn’t deserve to lose because we were the best team, because we played the best football, because we dominated the whole game,” Mourinho said.
Arsenal reaped some early reward from their decision to spend a club record 50 million euros (US$66 million) on Mesut Ozil on transfer deadline day. The Germany international set up Olivier Giroud for the opener, before in-form Aaron Ramsey scored twice in a 3-1 win at Sunderland.
A third straight win maintained Arsenal’s resurgence after a demoralizing opening-day defeat to Aston Villa.
“You’ve seen what he is all about, slipping those balls in,” Ramsey said of Ozil, who was substituted after 80 minutes on his debut. “He has one of highest assist rates in Europe and he is going to create a lot of opportunities for us.”
Manchester City’s mixed start to the season continued when they scraped a 0-0 draw at Stoke City.
Tottenham Hotspur began life without Gareth Bale, who joined Real Madrid two weeks ago, by outclassing Norwich City 2-0 with a double from Gylfi Sigurdsson, who was set up for his first goal by new signing Christian Eriksen.
Arsenal and Tottenham are level on nine points, while the Manchester rivals United and City are both on seven.
Elsewhere on Saturday, France international Hatem Ben Arfa scored one and set up another as Newcastle United beat Aston Villa 2-1 away for their second victory in a row.
West Bromwich Albion claimed their first point of the season by scoring in stoppage-time for a 1-1 draw at Fulham, while Hull City drew 1-1 with Cardiff City in a match between two promoted clubs.
The Gunners benefited from a debatable call at the Stadium of Light when the score was 2-1.
US international striker Jozy Altidore beat Bacary Sagna to the ball and prodded home a finish, only for the referee to bring play back for an earlier foul against Arsenal.
It was too much for combustible Sunderland manager Paolo di Canio, who was sent from the dugout in stoppage-time.
“He [the referee] came to me and said if you keep going with your manner, I send you up to the stand,” Di Canio said. “I said to him: ‘If you want to complete a perfect job, you send me off,’ and that is what he did.”