The 314th-ranked Indian dispatched Nishioka 7-6(10-8), 6-3 in an hour and 40 minutes in the second round contest.
Yuki saved as many as seven break chances on his serve against the Japanese, who is ranked 165 in the world.
The 22-year-old had ousted 129-ranked and 15th seed Evgeny Donskoy of Russian in the opening round.
He is now up against the United States' Chase Buchanan, who knocked out Croatia's 32nd seed, Mate Delic, 4-6, 6-1, 6-4 in his second round match.
It will be the first meeting between Yuki and Buchanan, who is ranked 179.
Somdev Devvarman and Ramkumar Ramanathan had bowed out in the first round of the qualifiers.
Image: Yuki Bhambri