New Zealand striker Chris Wood came off the bench to earn promoted Leicester City a dramatic 2-2 draw at home to Everton in his side's first top-flight game since 2004.
After Leicester new recruit Leonardo Ulloa had cancelled out Aiden McGeady's precise 20th-minute opener, Steven Naismith looked to have given Everton victory, only for Woods to fire home four minutes from time.
Tottenham's Eric Dier enjoyed a dream debut by scoring a 93rd-minute winner in a 1-0 success at West Ham United after Kyle Naughton, for the visitors, and James Collins, for the hosts, had both been sent off.
There was also late excitement at The Hawthorns, where new West Bromwich Albion manager Alan Irvine was denied victory against Sunderland by an 85th-minute goal from Sebastian Larsson.
West Brom led 2-1 after Saido Berahino replied to Lee Cattermole's 25-yard strike with a brace, but Larsson earned Sunderland a 2-2 draw by sweeping home a cut-back from debutant Patrick van Aanholt.
James Chester's 52nd-minute header gave Hull City a 1-0 win at promoted Queens Park Rangers, while Andreas Weimann earned Aston Villa a 1-0 victory at Stoke City.
Later on Saturday, last season's FA Cup winners Arsenal will begin their campaign at home to Crystal Palace.
With manager Tony Pulis having left Palace on Friday after a reported disagreement with co-chairman Steve Parish, assistant coach Keith Millen will be in temporary charge for the trip to the Emirates Stadium.
Champions Manchester City travel to Newcastle United on Sunday, with Liverpool, the side they pipped to last season's title, hosting Southampton. Chelsea, third last season, visit promoted Burnley on Monday.
