The Hammers, who impressed in defeat at Manchester City last week, beat Antonio Conte's men at the London Stadium thanks to Marko Arnautovic's early goal.
The Austrian nipped in behind Andreas Christensen and, as Cesar Azpilicueta stood off, curled his shot around the defender and keeper Thibaut Courtois.
"The win was the biggest thing, to get a win in the Premier League is really hard especially against the champions," the Scot said to Sky Sports.
"The spirit of the team, how they stuck together pleased me. The basics were in the main done well.
"I got a big boost from the performance at Manchester City, we didn't take any points from it, but there was something to talk positive about.
"We look harder to beat at the moment, we have people who can create and score goals so if we can get the back end sorted we might give ourselves a chance of earning some points.
Hammers skipper Mark Noble praised the effect Moyes has had since he arrived at the club.
"We have got a great bunch of players who work hard for each other," he said.
"We didn't have the rub of the green in the first part of the season, but I think the manager has come in and solely concentrated on the team shape and not conceding goals and I think that showed today.