London:David de Gea saved a 95th minute penalty from West Ham's veteran midfielder Mark Noble to give Manchester United a dramatic 2-1 win in the London Stadium. Manchester United had fought back from a goal down after Said Benrahma had put West Ham ahead after 30 minutes.
Cristiano Ronaldo equalised from close range six minutes later after West Ham keeper Lucas Fabianski had saved his original header and Jesse Lingard, who had a successful loan at West Ham last season, curled home the winning goal in the 89th minute.
Luke Shaw's handball deep into injury time gave West Ham the chance to level the score, but De Gea saved from Noble, who was brought on specifically to take the penalty.
Chelsea went to the top of the table after a dominant display gave them a 3-0 win away to Tottenham in the last game of the weekend.
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Tottenham threw everything at Chelsea in a high-tempo first half, but all of their efforts were undone when Thiago Silva headed Chelsea ahead following a corner in the 49th minute.
N'Golo Kante celebrated his return from an ankle injury by hitting his side's second of the game in the 57th minute with a big deflection off Eric Dier, and Antonio Rudiger rounded off the win with a smart finish in injury time.
Earlier on Sunday, Brighton confirmed their excellent start to the season with a 2-1 win over Leicester City thanks to a Neal Maupay penalty and Danny Welbeck's header.
Jamie Vardy got a goal back for Leicester on his 250th Premier League appearance, but the visitors were frustrated when Ademola Lookman and Wilfred Ndidi had goals ruled out for offside.
Sadio Mane's 100th goal for Liverpool helped his side to a 3-0 win at home to Crystal Palace that was tougher than the final score suggests.