Chennaiyin captain Anirudh Thapa (74th) sealed the deal with a fine strike.
Sahal Abdul Samad missed an easy chance for Blasters early in the second half.
The Blasters had lost their season opener, 2-4 to ATK Mohun Bagan.
Bengaluru FC beat NorthEast United FC 4-2 In an entertaining contest that saw six different goalscorers.
ATK Mohun Bagan edged out NorthEast United FC 2-1 in the play-offs second leg to register a 3-2 aggregate win.
Idrissa Sylla headed in a stoppage-time header to help NorthEast United hold ATK Mohun Bagan to a 1-1 draw in the play-offs first leg.
Blasters ended their campaign in 10th place with 17 points.
Three teams – Hyderabad FC, FC Goa and NorthEast — are tied on 27 points from 18 games, intensifying the race for the last two play-offs spots.
While Hyderabad moved to third on goal difference, NEUFC climbed above FC Goa to fourth.
NEUFC eventually grew into the game and fashioned better chances in the second quarter of the opening half. They had a penalty claim denied after the half-hour mark.