Chelsea boss Maurizio Sarri meanwhile admitted that Rice, and the rest of West Ham's defence, had successfully frustrated his attacking stars, who failed to score in the Premier League for the first time this season. In this period, it's not a big problem.
"We have to work and then, maybe, in one year we will be at the same level as Liverpool'".
The experienced stopper is quickly becoming a favourite of the West Ham crowd through his performances. Olivier Giroud won his battle with Alvaro Morata for a starting spot up front for Chelsea, keeping his place for the second Premier League match in succession.
It was the well-documented moment, two years ago, when Antonio Conte finally settled on the 3-4-3 shape that kick-started Chelsea into a title-winning machine, which thrust the unlikely wing-back pair of Marcos Alonso and Victor Moses into influential roles on either flank.
Chelsea controlled the ball for most of Sunday's game, but chances were few and far between, with West Ham looking the more likely to win for much of the game.
Chelsea finished the half with a flourish, but N'Golo Kante's header from Willian's cross went just wide.
Speaking after his latest impressive showing, Manuel Pellegrini said Rice had "taken his chance" with the senior team, and highlighted the fact the best was yet to come with the youngster still learning his role. I am surprised. In Naples, the first month was very hard. I don't think so. "In the last two or three matches we've defended very well, but we have to improve in the offensive phase especially in this kind of match". I want to see the picture tomorrow during our training session. "I don't know, maybe I will change 11, maybe five".
Information from The Associated Press was used in this report.