What an impressive win not just winning however. This was a team with a plan, building on the narrow defeat at Manchester City. It was a team which matched, even surpassed, their counterparts for running and energy.
Here was Marko Arnautovic, challenged by his manager to prove himself, sprinting in behind a Chelsea back three and causing endless problems. And there was Michail Antonio doing the same and seemingly putting the debacle of his last-minute error at Crystal Palace, so damaging for him and his team, behind him.
And here were the Premier League champions looking, frankly, tired and short of ideas. Whereas a late change had revived them at Liverpool, here West Ham contained them. There was an awful moment for the home fans on 82 minutes when Alvaro Morata looked sure to score. But otherwise it was a performance quite apart quite distinct from what you might expect.
This was the 41st consecutive Premier League matchday in which Moyes started in the relegation zone, setting a new record, but his West Ham side showed plenty to suggest that they are by no means a lost cause during the first half.
They had the lead within six minutes thanks to a well-worked goal from Marko Arnautovic, his first for the club, before sitting deeper and looking solid at the back.
MATCH FACTS AND STATS
West Ham (3-4-3): Adrian 7; Reid,7, Ogbonna, 7.5, Creswell, 7; Zabaleta, 7, Obiang, 7, Noble, 7, Masuaka, 8; Lanzini, 7.5, Antonio, 7.5, (Ayew 79, 6.5) Arnautovic, 8.5 ,(Sakho, 69, 6.5);
Subs not used: Carroll, Hernandez, Hart, Fernandes, Rice
Goalscorers: Arnautovic (6)
Booked: Arnautovic, Adrian, Reid, Cresswell, Obiang, Masuaku
Manager: David Moyes
Chelsea: (3-5-2): Courtois 6; Cahill, 5.5, Christensen, 5, Azpilicutea, 5.5; Zappcosta, 5.5, (Willian 64, 6)Fabregas, 6, Kante, 6, Bakayoko, 5 (Pedro, 45, 6), Alonso, 5 (Moses 6); Hazard, 6, Morata 5;
Subs not used: Caballero, Rudiger, Batshuayi, Ampadu
Manager: Antonio Conte
Referee: Anthony Taylor