Yuki ended the campaign of compatriot Prajnesh Gunneswaran with a 6-4 6-2 win in an all-Indian first round contest at the hard-court event.
Balaji, who had made an impressive Davis Cup debut against Uzbekistan, knocked out local wild card entrant Farrukh Dustov 6-3 6-1.
However, Ramkumar, who recently made his first ever Challenger level final in Tallahassee, went down fighting 4-6 4-6 against Italy's Cem Ilkel.
Ramkumar is ranked 216 while his opponent is placed 326 in the ATP singles ranking chart.
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