Chhetri (61st minute) scored his fourth goal of the tournament before Mahesh Singh (70th) struck to notch up the home side's second consecutive win.
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.
Chennaiyin FC became the third team to reach 50 wins in the ISL after they beat ATK Mohun Bagan in their opener. Get live streaming details of Chennaiyin FC vs Bengaluru FC.
'Better late than never' for the Manipuris as the city is set to host the Indian National Football team for the first time.
FC Goa enjoy 10-8 head-to-head record against Chennaiyin FC in ISL. Get CFC vs FCG live streaming details.
ATK Mohun Bagan have won two of their four meetings with Chennaiyin FC with two games ending in draws. Get live streaming details.
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.
Hyderabad FC now have six points from two matches while Chennaiyin have one from the same number of games.
Chennaiyin FC are tied with ATK Mohun Bagan on 15 points and sit at seventh in the ISL 2021-22 standings. ATK Mohun Bagan are sixth.