Broady, 18, will play Canadian Filip Peliwo in Sunday's final after he beat another Japanese Yoshihito Nishioka 6-4 6-0.
Thirteenth seed Broady will look to match the achievement of Oliver Golding, who won the boys' singles at Flushing Meadows last year, and Andy Murray, who won it in 2004.
However Peliwo is second seed and this year's Wimbledon champion.
Another Briton, Kyle Edmund, partners Portuguese Frederico Ferreira Silva in the boys' doubles final on Saturday against Australians Nick Kyrgios and Jordan Thompson.
