Yuki, ranked 216, fought off the challenge posed by Japanese qualifier 6-1 4-6 6-3 after battling for one hour and 53 minutes.
244th ranked Myneni, who is struggling due to bad stomach for the last couple of days, could even complete the first set as he quit the contest when he was trailing 2-5 against Japanese Hiroki Moriya, ranked 170.
Yuki made a superb start and looked like running away with the contest but the Japanese fought back and broke the Indian twice to take the second set.
"I started really well but let him comeback. I felt I was always in control of the games but he kept fighting and won points at the right time which helped his confidence in the second set," Yuki said.
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"I was trying to push for that one break in the third set and finally got it at 4-3. But he mixed it up really well by coming to the net and made it a harder match," the Delhi lad said.
Myneni, who will pair up for doubles with Yuki, said he was still not sure of playing tomorrow.
"I have to see how I feel tomorrow. I have not been well for a week now and I need to be careful about my health too," Myneni said.