Yuki, ranked 314th, knocked out Russian 15th seed Evgeny Donskoy 4-6, 6-1, 8-6 in his first round match at Show Court 2.
The 22-year-old now faces Japanese Yoshihito Nishioka, who outplayed Chile’s Gonzalo Lama 6-2, 6-1.
Nishioka is placed 149 places above Yuki but the Indian will take confidence from the fact that in Donskoy he beat somebody who is ranked as high as 129th.
Somdev, who is going through a very lean patch, lost 4-6, 6-3, 4-6 to lower-ranked American Austin Krajicek.
The 284th-ranked Ramkumar went down fighting to 254th-ranked Nils Langer of Germany 5-7, 6-4, 4-6 in his opening qualifying round of the first Grand Slam of the season.