Spurs raced into a 2-0 lead inside 27 minutes at the City Football Academy. Shayon Harrison scored first with a free-kick before Kazaiah Sterling headed in Jaden Brown's cross.
But Foden, who made his senior debut in the UEFA Champions League in midweek, started the comeback with a fine dribble and finish on 33 minutes.
Nmecha equalised shortly after half-time, curling into the top corner, and the 18-year-old striker won it with two more goals in the final 10 minutes.
City climb to eighth, while a third straight loss leaves Spurs bottom.
Man City: 10 Dec v Arsenal (H) PL2
Spurs: 11 Dec v West Ham (A) PL2