West Ham manager David Moyes celebrated his first win in charge as champions Chelsea slumped 1-0 to suffer another dent to their Premier League hopes.
Marko Arnautovic's early goal ended an eight-game league winless run for the Hammers, who had lost three of four since former Everton and Manchester United boss Moyes replaced Slaven Bilic last month.
It was Chelsea's first defeat in seven top-flight matches and afterwards boss Antonio Conte conceded his team are now out of the title race as they lie 11 points adrift of leaders Manchester City.
"This is the fourth defeat in 16 games. When you have these stats it's impossible to think you are in the title race," the Italian said.
"If you want to stay in the race for the title in the first part of the season you can only lose once or twice."
Despite the win, the Hammers remain in the relegation places, though only on goal difference behind West Brom.
But boss Moyes admitted he was relieved to get his first all-important three- point haul.
"The win was the biggest thing, to get a win in the Premier League is really hard especially against the champions," Moyes said.
"We have people who can create and score goals so if we can get the back end sorted we might give ourselves a chance of earning some points."
Tottenham host Stoke and Leicester visit Newcastle among Saturday's six other matches.
Meanwhile Scott Arfield's goal on the stroke of halftime was enough to give seventh placed Burnley a 1-0 win over eighth placed Watford.
Pre-match snow made for wintry conditions at Turf Moor for the clash of two of the surprise packages of the season so far and it was Scottish-born Canadian international Arfield, in for the injured Robbie Brady, who rose to the occasion.
Iceland winger Johann Berg Gudmundsson's low cross was well collected by Arfield who beat his marker and delivered a slick finish to beat Huerelho Gomes in the 45th minute.
Watford had been down to ten men from the 39th minute after Marvin Zeegelaar was shown a straight red for a wild challenge on Steven Defour. Burnley had two efforts disallowed for offside in the second half.