Eighth seed Yuki pipped fourth seed Japanese Tatsuma Ito 6-4 1-6 7-5 in the quarterfinal, which lasted one hour and 46 minutes.
The 277-ranked Yuki avenged his last year's defeat in Kyoto against the higher-ranked Japanese, who is 105 places above the Indian in the ranking chart. Yuki next faces second seed and 138-ranked James Duckworth.
Yuki had lost to the Australian last week when they clashed in the quarter-finals of Melbourne Challenger.
Meanwhile, in the Charlottesville Challenger, second seed Somdev scored an easy 6-2 6-3 win over Denis Molchanov of Ukraine to progress to the next stage. He is now up against seventh seed American Rhyne Williams.
Joining him in the singles last-eight was Myneni, who brushed aside the challenge of American Chase Buchanan 6-4 6-4 in one hour and 22 minutes. He next faces Jesse Levine of Canada.
However, Somdev's campaign in the doubles competition ended in the quarter-finals. He and Sanam Singh lost 4-6 2-6 to second seeded Americans Austin Krajicek and Tennys Sandgren.