Everton were held to a 2-2 draw at newly-promoted Leicester City. Aiden McGeady scored a beautiful top corner strike to put Everton ahead but The Foxes twice came from behind to level the game with Chris Wood netting their second, four minutes from time.
Eric Dier scored on his debut to bag Tottenham a 1-0 win at West Ham where both sides finished with ten men.
Hull were 1-0 winners at QPR, with James Chester getting the game's only goal.
Andi Weimann scored as Aston Villa came away from Stoke with a 1-0 win.
West Brom and Sunderland evenly shared four goals at the Hawthorns.
And they may be under new management, but the same problems remain for Manchester United. The Louis Van Gaal era at Old Trafford began with a 2-1 defeat to Swansea City.
Final scores in the Premier League
Manchester United 1 Swansea 2
(Wayne Rooney 53' // Ki Sung Yueng 22', Gylfi Sigurdsson 73')
Leicester 2 Everton 2
(L: Leonardo Ulloa 22, Chris Wood 86 // E: Aidan McGeady 20', Steven Naismith 45')
QPR 0 Hull 1
(H: James Chester 52')
Stoke 0 Aston Villa 1
(AV: Andi Weimann 50')
West Brom 2 Sunderland 2
(WB: Saido Berahino 42'pen. 74' // S: Lee Cattermole 5', Sebastian Larsson 85')
West Ham 0 Tottenham 1
(W: Mark Noble missed pen 30', James Collins sent-off 63' // T: Kyle Naughton sent-off 29', Eric Dier)
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