Seventh seed Yuki regrouped after a disastrous opening set for 1-6 7-5 7-6(1) win over Serbia's Laslo Djere in the gruelling second round that lasted two hours and 21 minutes.
Saketh got past British qualifier Luke Bambrdige 6-3 6-2 in his second round in just 64 minutes.
Saketh faced only one break point in the whole match and that too he saved. He broke his rival thrice -- twice in in second set.
Yuki struggled to hold serve at the start, losing it three times to let Djere runs away with the opening set. However, the Indian youngster dug deep into his reserves and improved as the match progressed.
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"It was a real test against a genuine clay court player. Playing on clay is a different ball game altogether. He played really well in the first set and I did not have much of a shot. I decided to focus on my service games," Yuki said after his match.
"I made a few adjustments. I was still in hard court mode. I made more first serves and was a bit more patient in rallies as the balls comeback. Sliding on clay is a bit of alien to me so that got better too," he added.
Saketh is up against eighth seed Briton Brydan Klein.