Zverev, the victor, will meet in the final tournament in 2018, following the Australian Jordan Thompson or Croatian Borna Choric, who eliminated the Greek, Stefanos Tsetsipas, ranked sixth in the world, from the third round.
This is the first time that a German player has reached the quarter-finals of the US Open in 13 years.
The semi-finals of the Australian Open at the beginning of this year are considered the best result of Zverev in the Grand Slam tournaments when he came out against Austrian Dominique Thiem.
American Jennifer Brady, ranked 41 in the world, reached the quarter-finals of the Grand Slam for the first time in her career, beating German title holder Angelique Kerber in 2016, 6-1, 6-4 in the semi-finals.
Brady will next meet Kazakhstan’s Yulia Putintseva, who overtook 8th seed Petra Martic in the tournament and 15th in the world with a score of 6-3, 2-6, 6-4 in two hours and 37 minutes.