The scoreline remained 2-2 at the end of full-time and five minutes of added time despite the best effort of both sides to find the elusive winning goal.
Chhetri was shown the first yellow in the 22nd minute after bringing down Anirudh Thapa, something he repeated on the same player after nine minutes to be sent off.
SC East Bengal played most part of the second half with 10 men after captain Daniel Fox was sent off in the 56th minute.
Goals from Matti Steinmann (6th) and Anthony Pilkington (68th) secured the victory for SCEB
Former champions Chennai City FC defeated Gokulam Kerala FC 2-1 in their opening match of the I-League, Kalyani, on Saturday.
Both sides created chances in the first half but it was SCEB who converted them and deservedly headed into the break with a two-goal cushion.
NorthEast United inched closer to a playoffs berth with a 2-1 win over 10-man SC East Bengal in the ISL