Nwaneri, 17, prodded home from Raheem Sterling's cut back pass to make it 3-0 late in the match.
At 17 years and 247 days old, Nwaneri is only behind Cesc Fabregas, who remains Arsenal's youngest goalscorer in the top-flight at 17 years and 113 days.
Nwaneri made headlines when he came on as a substitute aged 15 in a 3-0 away win at Brentford in September 2022 but has continued to show lots of promise in a red shirt.
It was the youngster's third goal of the season after he scored a brace in the League Cup against Bolton in September.
After Nwaneri's brace against Bolton in September, boss Mikel Arteta admitted that 'the boy is ready'.
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Following Saturday's win over Nottingham Forest, Arteta said: 'He is the second youngest [Premier League goalscorer] in our history. That's a story in itself.
'He's brave. You see the reaction of fans and they were singing 'he's one of our own'' he added.
'I think we have to put brick by brick and make sure the cement doesn't get dry. Hopefully we can build a beautiful thing with him.
The goal sealed off an impressive, and important, win for Arsenal at the Emirates, seeing off an in-form Nottingham Forest with ease as the visitors looked at times struggling to get out of their own half.
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Bukayo Saka opened the scoring with a magnificent strike as he sailed past two defenders to slam into the top corner from Martin Odegaard's cool pass.
It marked Saka's third goal of the season in the top-flight, as well as his seventh assist.
Thomas Partey, who stepped in for Jorginho at half-time, doubled their lead with a curled in shot from 20 yards out and Nwaneri topped off a strong performance for the home side.
On the performance as a whole, Arteta had high praise for his substitutes: 'It was good to see the impact of the substitutes [Thomas Partey - goal; Ethan Nwaneri - goal; Raheem Sterling - assist]. Everyone has to feel important. It was a good afternoon.
Arsenal travel to Portugal to fave Ruben Amorim's former club Sporting in the Champions League on Tuesday, before a visit to West Ham United on Saturday.