The 314th-ranked Indian dispatched Nishioka 7-6 (10-8), 6-3 in one 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 also ousted 129th ranked and 15th seed Evgeny Donskoy from Russian in the opening round.
Yuki is now up against America's Chase Buchanan, who knocked out Croatia's 32nd seed Mate Delic 4-6 6-1 6-4 in his second round.
Somdev Devvarman and Ramkumar Ramanathan had bowed out in the first round of the qualifiers.