West Ham In Shock 1-0 Win Over Arsenal
“He is improving in every game,” Pellegrini told Sky Sports.
“He has showed good technique and is good in aerial duels, I think we are seeing the complete player. At 19 years old, I am sure we will see a top, top player.”
Rice beat Bernd Leno with a first-time shot after a good lay-off by Samir Nasri, who was making his first top-flight appearance in England since August 2016.
The maiden top-flight goal comes two weeks after Rice signed a new contract that will keep him with the Hammers until 2024.
Before that, the international future of Rice, who can play at centre-back or in centre midfield, had been in the headlines.
He has earned three caps for the Republic of Ireland, all in friendlies, and the London-born man could yet decide to declare for England.
In a highly-competitive London derby, Alexandre Lacazette was denied by an excellent save from Lukasz Fabianski as Arsenal failed to score in the league for the first time since the opening day of the season.
West Ham were full value for their win, with Marko Arnautovic, Rice, Nasri and Felipe Anderson all going close when the game was goalless.
While West Ham move up to eighth in the table after a sixth win in nine league games, Arsenal remain fifth.
The Gunners are three points behind fourth-placed Chelsea, who entertain Newcastle at 17:30 GMT.
This was a result to remember for Manuel Pellegrini and West Ham, with the performance a fitting way to mark 50 Premier League games at London Stadium.
Bournemouth, Wolves, Tottenham, Manchester City and Watford have all won at the venue this season.
Yet the Hammers turned in one of their best performances under Pellegrini to claim a first win over Arsenal since 2015.
Nasri brought an air of authority and added quality to the midfield while Marko Arnautovic was busy and inventive despite the player’s agent and brother saying the Austrian striker wants to move to a Chinese club during this transfer window.
The 29-year-old did, however, wave to fans when he was replaced with 20 minutes to go.
West Ham are not home again until 4 February – after the transfer window closes – and if Arnautovic was saying his goodbyes, at least West Ham’s future is bright in the shape of Rice.