Myneni, playing against fellow wild card entrant Karunuday Singh, won 7-5 6-2 after battling for close to two hours on the slow and bouncy centre court at R K Khanna tennis stadium.
Karunuday had chances galore in both the sets but could not go on top against Myneni, the country's number two singles player at number 258.
Vardhan, who earned the wild card thanks to his national championship win in October 2014, lost 4-6 5-7 to Serbia's Pedja Krstin.
Prashanth humbled Spanish top seed Jamie Pulgar-Garcia 6-2 6-2 in just 65 minutes while Balaji got past Australia's Andrew Whittington 7-5 6-4 in one hour and 19 minutes.
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Myneni was far from playing his best game as he himself admitted that he took some time to find rhythm due to the slow nature of the court, which was completely different from the surface he played in the last few weeks in Australia and Hong Kong.
With strong wind having an impact on his shots, Myneni dropped serve in the third game of the opening set, albeit after saving five break points. The lanky Indian struggled with his first serve and handed his compatriot lead when he netted a backhand on the sixth break chance.