Essien's goals were his first since for the club since he tore the medial ligament in his left knee while training with Ghana before the African Nations Cup in January.
Essien headed them in front in the second minute and then made it 3-0 with another seven minutes from time.
Sandwiched in between was a bizarre goal for Salomon Kalou after West Ham goalkeeper Robert Green and centre-half Matthew Upson failed to clear Didier Drogba's 30-yard free-kick.
West Ham midfielder Scott Parker scored a late consolation goal, the first Chelsea have conceded all season, but, as far as Ancelotti was concerned, it could not take the shine off Essien's performance.
"I think he's better than a new signing," said Ancelotti. "We missed him last season because he's one of the top midfielders in the world. He came back and we're happy he can maintain this level of play.
"He's fit now. We have to pay attention because he's playing well, all the games at the start of the season. He scored today, and that's fantastic. He's a fantastic jumper and I hope he maintains this position for as long as possible."