Moyes’ side moved five points clear of the relegation zone thanks to Joao Mario’s opener and two goals from Marko Arnautovic.
After West Ham’s recent home defeat by Burnley was overshadowed by pitch invasions, missile-throwing and protests in front of the directors’ box, there were real fears of more unsavoury scenes.
Fans staged a protest march against co-owners David Gold and David Sullivan before kick-off, but a truce was called inside, mostly due to West Ham’s improved performance.
“The players showed how they felt about past events, they were pent up and ready to go,” Moyes said.
“I thought before kick-off the supporters showed they are with the club and with the team, and then the players showed what they were going to do. They really kicked on.
“It was a really big game for us, if we’d lost we could have slipped further down.
“We won’t get carried away, but we’ve not dropped into the bottom three. There are some big games to come and if the stadium stays like it was today it gives us a great chance.”
Despite the ill-feeling towards Sullivan and Gold, both were in attendance, although they took seats further back than usual in a directors’ box protected by extra security.
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