Singh prevailed 3-6, 7-5, 6-4 in an hard-fought contest.
In the other men's singles matches, fourth seed Nitten Kirrtane, a former national champion, won the first set 6-2 and was leading 2-0 when his opponent Arpit Sharma retired. Second seed Vishnu Vardhan got the better of Saran Sai Reddy 7-5, 6-4.
In the women's singles, top seed Rishika Sunkara looked at ease as she had an easy passage into the second round with a 6-3, 6-4 win over C Sai Samhita. Seed two Shweta Rana moved to the next round after an easy win of 6-1,6-2 over Nithya Raj Baburaj.
Earlier in the day, Mukund played with great determination as he took the lead in the first set before Singh fought his way back into the match to draw level.
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Mukund looked good in the decider and broke Singh early in the third game but could not continue his brilliant form because of the back pain that affected his game at the crucial stage of the match.
Mukund had to call for medical attention after the seventh game of the third set and thereafter, he was not the same player. The medical time-out gave Singh ample time to regroup his thoughts and he sealed off three straight games to win his opening round match.
After winning the first set 6-3, Mukund had his chances in the second set as well but Singh, who hasn't played much in the last six months, got his act together in time to force the match into the third set.
Garvit Batra defeated Lakshit Sood 6-4, 1-6, 6-4 in the other men's singles match, V M Ranjeet and P C Vignesh also recorded comfortable victories against Vinod Sridhar and Ajay Yadav respectively. While Vignesh thrashed Yadav 6-3, 6-3, Ranjeet defeated Sridhar 6-4, 6-2.