The eighth seed Indian overcame the challenge of the Kiwi player 1-6, 6-3, 7-6(4) in the second round match of the $50,000 hard court tournament.
Yuki dropped his serve twice in the opening set but came back strong as he broke Venus in the second set to take the match to full length.
There was no break-of-serve in the deciding third set, in which Yuki prevailed in the tie-breaker after one hour and 56 minutes contest.
The 277-ranked Yuki will now face 172-ranked Japanese Tatsuma Ito, who is leading head-to-head record 1-0.
Yuki had lost to the Japanese last year in Kyoto. Meanwhile, in the Charlottesville Challenger tournament in the United States, Somdev Devvarman and Sanam Singh reached the doubles quarter-finals with a straight set win over local wild cards Mitchell Frank and Mac Styslinger.
The Indians beat the Americans 6-2, 6-3 in just 55 minutes to set up the quarter-final match against second seeded American pair of Austin Krajicek and Tennys Sandgren.
Image: Yuki Bhambri
Photograph: Quinn Rooney/Getty Images
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