24-year-old Yuki, who won the junior Australian Open title in 2009, saved all the three breakpoints in the match that lasted 68 minutes.
The Indian youngster broke his rival once in each set, and remained solid throughout.
His next opponent is 21st seed American Ernesto Escobedo, who brushed aside Tatsuma Ito from Japan 6-1 6-3 in his second round match.
"I played well today. It was another good win for me. I served good and broke him at crucial times and that is what made the difference," Yuki said after the match.
Saketh Myneni exited in the first round after encountering a foot problem.
"I have to fight with myself before fighting with the other person across the court," Myneni said.
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