Manchester City went back to the top of the Premier League on Sunday despite a 1-1 draw with Southampton that left them winless in five games.
Arsenal hit top spot in the Premier League on Saturday but were still frustrated as they could only draw 0-0 with struggling Middlesbrough.
Maarten Stekelenburg saves two penalties as Everton draw 1-1 with Premier League leaders Manchester City.
Manchester United manager Jose Mourinho was left to rue his side's wastefulness in front of goal as they were held to a 1-1 draw at home by lowly Stoke City on Sunday.
Personnel from three clubs in England's second-tier Championship have been linked with corruption allegations in an undercover newspaper investigation.
Manchester United bounced back to form with a 4-1 thrashing of champions Leicester on Saturday to move up to third in the Premier League, for a few hours at least.
Manchester United manager Jose Mourinho admitted his side have to improve after they suffered their third defeat in eight days with a 3-1 loss at Watford on Sunday.
Manchester City crushed Bournemouth 4-0 on Saturday to extend their lead at the top of the table to five points with a fifth win out of five.
Chelsea lost their perfect record in this season's Premier League after an entertaining 2-2 draw at Swansea on Sunday.
Manchester City threw down an early marker in the Premier League title race by beating rivals Manchester United 2-1 on Saturday.
Substitute Marcus Rashford scored an injury-time winner as Manchester United beat Hull City 1-0 on Saturday.
Manchester City completed the signing of Barcelona goalkeeper Claudio Bravo for 18 million euros (15.4 million dollars) on Thursday.
Bastian Schweinsteiger said Wednesday that Manchester United will be his final European club even though he's fallen out of favour with manager Jose Mourinho.
West Ham made a winning Premier League debut in their new stadium on Sunday while promoted Middlesbrough picked up their first victory of the young season.
Late goals were the order of the day on Saturday as Manchester City and Chelsea maintained their winning starts to the Premier League season.