The 1-0 success at London Stadium was the fifth time in the last six matches that a team managed by Moyes have triumphed at home against the reigning Premier League champions.
Everton then earned a 1-0 win over Carlo Ancelotti’s Chelsea the next season but lost to United in October 2011.
Next followed home wins over three more title-winning Italian managers: Roberto Mancini and Manchester City in 2012/13, then for Sunderland against Claudio Ranieri’s Leicester City in 2016/17 before West Ham beat Antonio Conte’s Chelsea on Saturday.
"The spirit of the team, how we stuck together and our effort was fantastic," Moyes told West Ham’s official website. "The basics were done very well today."