Moyes grabbed the 200th win of his career to join Sir Alex Ferguson, Arsene Wenger and Sir Harry Redknapp.
Ferguson was in the crowd as Moyes secured that win and the Hammers boss declared: “It was a much better performance. A bigger threat and we passed it well at times.
He added: “For us to beat one of our rivals is a big thing. I don’t think any of the teams are much better than the other so the games are going to be close, but we’re beginning to win on the road.
“We won at Stoke and here and we’ve started to get a wee bit of form at the London Stadium as well. Hopefully that will bode well between now and the end of the season.”