West Ham beat Arsenal 1-0 at the London Stadium on Saturday (Image: GETTY)
The 19-year-old scored his first goal for West Ham as Manuel Pellegrini's men once again exposed Arsenal's soft underbelly.
Hammers youngster Rice was presented with a glorious opportunity early in the second half when Granit Xhaka's poor headed clearance fell to him in the area.
The midfielder, who has yet to choose between England and the Republic of Ireland over his international future, was never going to miss and he duly tucked the ball home.
The display left Jenas purring as he raved on Match of the Day: "He's going from strength to strength actually.
Declan Rice was overjoyed after scoring his first professional goal (Image: GETTY)
To take that goal so instinctively at such a young age, it was a really complete display
Jermaine Jenas on Declan Rice
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"To take that goal so instinctively at such a young age, it was a really complete display - and a really mature display."
It was the perfect early birthday present for Rice, who turns 20 on Monday
Hammers boss Manuel Pellegrini said: "I am sure Declan will be a top player.
"He is improving in every game, he is now more used to giving us a good build-up in front and not so many passes backwards.
Rice is yet to decide if he wants to represent England or the Republic of Ireland (Image: GETTY)
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"Declan is very strong in aerial duels, he is strong one-versus-one, has a good technique, and he demonstrated that in the goal he scored.
"So I'm sure that we are seeing a top player soon and we'll see not only for West Ham but also for the national squad that he decides to play for.
"Maybe in this position he can score more goals but the second step for him to continue improving is to try to have a good view of all the pitch.
"That is where we are working with him in every way."