Midfielder Anirudh Thapa (15') and Vafa Hakhamaneshi scored in each half to take Chennaiyin FC past the hosts and into the knockout stage of the competition.
Playing in Arthur Ashe Stadium, the 24-year-old played fearlessly throughout the three-hour, 31-minute thriller to clinch the match against Nadal 6-4, 4-6, 6-4, 6-3.
The Australian passed the stiff test against the Russian 7-6(11), 3-6, 6-3, 6-2, playing his aggressive game to triumph after two hours and 53 minutes.