Chhetri had put India on the road to victory with an injury-time strike in the first half but an own goal by Anwar Ali in the added time of the second half spoiled the home side's march.
Greg Stewart scored in the 40th, 100th and 118th minute while Lallianzuala Chhangte got a brace in the 78th and 94th minute for Mumbai City FC on Sunday.
Rahim Ali, Kwame Karikari, Anirudh Thapa and Sajal Bag were on the scoresheet as the Marina Machans clinched a third successive win for the first time this season and went level on points with FC Goa.
Rahim Ali has made 40 appearances for Chennaiyin FC in Indian Super League so far since joining the former champions three years back.
With two wins from two matches, FC Goa are now top of the table in the ongoing Indian Super League 2022-23. FC Goa play Hyderabad FC next.
