The Japanese took a goose egg in the first set and trailed 2-5 in the third before completing an unlikely 0-6, 6-4, 7-6 (2) victory in just over two hours for his first career top-10 win.
Mochizuki will look to continue his dream run on home soil in the quarterfinals against Australia's Alexei Popyrin, who outlasted Chile's Cristian Garin 4-6, 7-6 (3), 6-2 in the Round of 16.
Fourth-seeded Alex de Minaur faced only one break point in a 6-0, 7-5 win against Argentina's Diego Schwartzman. He will face Russia's Aslan Karatsev, a 6-3, 6-4 winner over China's Zhang Zhizhen.
European Open
Frenchman Hugo Gaston, the 96th-ranked player in the world, upset second seed Jan-Lennard Struff, ranked 27th, in the round of 16 in Antwerp, Belgium.
Gaston emerged from a battle, 5-7, 7-6 (5), 7-6 (11), despite Germany's Struff having a 15-9 advantage in aces. Gaston converted three of eight break points to just 4 of 16 for Struff.
Top seed Stefanos Tsitsipas of Greece dispatched Botic van de Zandschulp of the Netherlands, 7-5, 6-3. Fifth seed Yannick Hanfmann of Germany eliminated Dominic Thiem of Austria, 6-4, 5-7, 6-4, and qualifier Maximilian Marterer of Germany defeated Nuno Borges of Portugal, 6-3, 7-6 (3).
BNP Paribas Nordic Open
Elias Ymer won in his home country, knocking off qualifier Dino Prizmic of Croatia, 6-3, 3-6, 6-2 in the Round of 16 in Stockholm, Sweden.
Ymer is ranked 168th in the world, Prizmic 165th. Ymer converted six of nine break points, Prizmic was 4 of 5.
The other three singles matches Thursday went two sets. Second seed Adrian Mannarino of France downed Russia's Roman Safiullin 6-4, 6-4; Tomas Machac of the Czech Republic got the better of Switzerland's Stan Wawrinka 6-4, 6-1; and Gael Monfils of France defeated qualifier Filip Misolic of Austria, 6-4, 6-3.
