Marko Arnautovic’s first Hammers goal was enough to give Moyes his first win in fifth game as West Ham boss at Chelsea’s expense
Chelsea boss Antonio Conte said his side’s fourth loss of the season, which left them 11 points behind leaders Manchester City, ruled them out of the title race.
Tottenham ended a four-game run without a league win by putting five past Stoke at Wembley, including two goals from Harry Kane.
Spurs are fifth and 15 points behind Manchester City, who face second-placed Manchester United in a derby match on Sunday (16:30 GMT).
Swansea lifted themselves off the bottom with Wilfried Bony’s late goal the difference in a 1-0 win over West Brom.
Paul Clement’s side moved above Crystal Palace, who saw Christian Benteke miss an injury-time penalty in a 2-2 draw with Bournemouth – both Cherries goals coming from 35-year-old Jermain Defoe.
A Steve Mounie double gave Huddersfield a 2-0 win over Brighton and moved them five points clear of the relegation zone but Newcastle lost 3-2 at home to Leicester in Saturday’s late kick-off.
Burnley moved level on points with fifth-placed Spurs and sixth-placed Arsenal – who face Southampton on Sunday (12:00) – by overcoming Watford with a Scott Arfield goal.
Results of Saturday Premier League Games
West Ham 1-0 Chelsea
Tottenham 5-1 Stoke
Crystal Palace 2-2 Bournemouth
Huddersfield 2-0 Brighton
Swansea 1-0 West Brom
Burnley 1-0 Watford
Newcastle 2-3 Leicester
Credit: BBC