SC East Bengal played most part of the second half with 10 men after captain Daniel Fox was sent off in the 56th minute.
Chennaiyin went into the lead after Suhail Pasha's header took a deflection from Hira Mondal and went inside the net for an own goal.
The win took the Highlanders to the second spot with eight points as they remained unbeaten from four matches.
After three losses on the trot, laggards SCEB finally opened their account
Jordan Murray put Kerala ahead in the 64th minute before Neville's stoppage-time equaliser (90+5) ensured that SCEB extended their unbeaten run to six games.
SC East Bengal gave a better account of themselves after the drinks break in the first half. They almost scored the equaliser but a save from Laxmikant Kattimani and a goal-line clearance from Joao kept the Hyderabad lead intact.
VP Suhair and Patrick Flottmann scored to give NorthEast the win.
The Sergio Lobera side now have six points from three matches, while SC East Bengal remained at the bottom of the table, yet to open their account in their debut ISL season.
SCEB failed to make use of a numerical advantage to settle for a 1-1 draw against FC Goa
Former champions Chennai City FC defeated Gokulam Kerala FC 2-1 in their opening match of the I-League, Kalyani, on Saturday.
As in their last match against Kerala Blasters, ATKMB struggled to get going initially, while SCEB made some fine attacking moves but lacked the finishing touches.
Goals from Matti Steinmann (6th) and Anthony Pilkington (68th) secured the victory for SCEB
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.
East Bengal finished the season in the bottom-place on the points table, with only one win in 20 matches
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.
Roy Krishna powered ATK Mohun Bagan to a 3-1 win over SC East Bengal
With the draw, Hyderabad are at third spot with 24 points from 17 matches while SC EB are at ninth with 17 points
A fearless competitor who used brain and brawn in equal measure, Subhas Bhowmick was one of the most fascinating characters in Indian football through the 1970s with his muscular built and equally expressive carefree opinions.
NorthEast United inched closer to a playoffs berth with a 2-1 win over 10-man SC East Bengal in the ISL
Adam Le Fondre put Sergio Lobera's men further ahead in the 59th minute as Hyderabad tasted their first defeat of the season.