The top seeded Indian posted a 6-0 7-6(5) win in the second round, which is only his fourth competitive match after returning to action following a six-month injury break.
Yuki, who is now ranked 283, broke his rival thrice to snatch the opening set from Gonzales. They traded a break each before Yuki prevailed in the tie breaker.
The Delhi lad, who featured in top-100 around this time last season, next faces fifth seed German Sebastian Fanselow.
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