Bizarre West Ham goal sinks Chelsea as Liverpool top Premier League
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On a day when all the title contenders are in action, champions Manchester City can claim top spot if they beat struggling Watford in the late kick-off.
Elsewhere, Newcastle won for the first time in the league this season to clamber off the bottom of the table and give new manager Eddie Howe hope they can survive.
Thomas Tuchel's Chelsea had lost just once in the Premier League before Saturday's match at the London Stadium and had conceded just six goals in 14 matches.
The European champions led twice, through a Thiago Silva header and Mason Mount's spectacular volley, but they were pegged back both times by a penalty from Manuel Lanzini and Jarrod Bowen's strike.
And with three minutes remaining substitute defender Masuaku, lurking out on the left wing, swung a speculative effort towards the Chelsea goal, deceiving Edouard Mendy as it arched past the stunned goalkeeper.
"So, was it a cross or was it shot," Masuaku asked on Twitter. "(Hint: I was as surprised as you)."
Tuchel bemoaned Chelsea's individual errors and the "freak goal" that led to their defeat.
"We hate to lose, we have to digest it now," he told the BBC. "It is not a performance to be mad about, but in detail we need to be better again.
"If we won the game nobody would have given us the title and if we lose it I don't think anybody else gets it this weekend."
West Ham, who had already ended Liverpool's long unbeaten run this season, consolidated their place in the top four but manager David Moyes urged his side to be more consistent.
Liverpool left it until the dying seconds to see off tenacious Wolves 1-0, with substitute Divock Origi firing home Mohamed Salah's pass in the 94th minute to take the visitors one point clear of Chelsea at the top of the table.
The visitors dominated possession at Molineux and had 17 shots on goal but Wolves battled hard to keep them at bay before Origi's late intervention.
"Divock Origi, the legend, finished it off and it's a great story," Klopp told Sky Sports. "He's an incredible striker. For different reasons he did not play that often but I hope one day he finds a manager that plays him more than I do.
"He's one of the best finishers I've ever seen in my life."
Newcastle scrambled a vital 1-0 win against fellow strugglers Burnley to move within three points of safety.
The decisive moment came late in the first half when goalkeeper Nick Pope spilled Joe Willock's cross as he came through a crowd of players.
Callum Wilson steadied himself before firing into the roof of the unguarded net and his strike survived a VAR check.
Howe said he was confident the team could stay up despite a testing run of fixtures coming up, adding that the January transfer window would be crucial.
"People above me are planning for that (January)," he told the BBC. "But my sole focus is coaching the team. I love working with this group.
"They are hungry and want to achieve. For sure we can stay up. We have come in from a difficult position and there is a long road ahead but I believe in what we are doing."
Brighton's Neal Maupay scored in the 98th minute to earn his side a 1-1 draw against Southampton.