Leicester City became the first English league champions for 27 years to begin their title defence with a loss as they went down 2-1 at Hull City on Saturday and Pep Guardiola's Manchester City reign started with a 2-1 win over Sunderland.
Hull's Robert Snodgrass got a 57th-minute winner as Claudio Ranieri's Leicester lacked the intensity of their last campaign while City got away with their lethargic display as Sunderland debutant Paddy McNair scored an 87th-minute own goal.
Leicester's shock defeat was the first time the title holders had lost their opening game since the Premier League was launched in 1992, while the last defending champions to lose their first fixture were Arsenal in 1989.
Hull's victory was a major boost for the club, who have only 13 fit first-team players and are still looking for a permanent manager after Steve Bruce quit on July 22, with interim coach Mike Phelan overseeing Saturday's victory.
Leicester winger Riyad Mahrez's penalty just after the break cancelled out Adama Diomande's acrobatic overhead kick in first-half added time before Snodgrass struck from inside the box.
"They played better," said disappointed Italian Ranieri. "We tried to do our best, our effort was amazing but it was individual, not as a team."
Guardiola's City career got off to a perfect start when Sergio Aguero fired home a fourth-minute penalty after Patrick van Aanholt had brought down Raheem Sterling.
Jermain Defoe thought he had rescued a point for Sunderland when he finished with aplomb in the 71st minute before McNair, under pressure from Kelechi Iheanacho, turned the ball past Vito Mannone four minutes after coming on for his debut.
"The first games are always difficult," said former Barcelona and Bayern Munich manager Guardiola. "We spoke during the week about what we had to do like a team and we did it."
Tottenham Hotspur's Erik Lamela put away an excellent header just before the hour mark to rescue a 1-1 draw for at Everton.
Ross Barkley had given new manager Ronald Koeman an ideal start to life at Goodison Park with a fifth-minute free kick.
Spurs lost their France keeper Hugo Lloris to a hamstring injury in the 36th minute of their disappointing first half but they bounced back when Lamela nodded in Kyle Walker's cross.
The visitors could have snatched a late winner but Everton keeper Maarten Stekelenburg denied new signing Vincent Janssen.
"The first half was difficult for us and we didn't play well," said Spurs manager Mauricio Pochettino.
"Hugo got injured and that had a big impact on us. In the second half we played as we usually play."
A debut goal for Nathan Redmond helped Southampton come from behind to secure a 1-1 draw at home to Watford while a late Leroy Fer strike gave Swansea City a 1-0 victory at promoted Burnley, who were fuming after a penalty claim was waved away.
Xherdan Shaqiri's free kick helped Stoke City to a 1-1 draw at promoted Middlesbrough after Alvaro Negredo's debut opener.
West Bromwich Albion won 1-0 at Crystal Palace thanks to a goal from Salomon Rondon.