A first half strike from Dimitrios Diamantakos resulted in a fourth straight win for KBFC, while hosts Jamshedpur FC slumped to their fifth straight defeat.
Hyderabad's goals came from three different players with Halicharan Narzary (65th minute), Chinglensana Singh (74th) and Borja Herrera (85th) getting themselves on the scoresheet. Petar Sliskovic (78th), on the other hand, scored for Chennaiyin.
The narrow win kept Odisha FC's 100 per cent record at home intact and helped them leapfrog Hyderabad FC and move into second place, three points behind leaders Mumbai City FC with a game in hand. NorthEast United FC remained at the foot of the table, still waiting to get off the mark.
In the 78th minute, Jerry Mawihmingthanga scored Odisha FC's 99th ISL goal to move the Juggernauts into the second position. Pedro Martin was benched in favour of Diego Mauricio, and the hosts only made one other alteration to their starting eleven.
In terms of head-to-head, Chennaiyin have won three against Hyderabad's two, with one game ending in a draw. When the two sides locked horns at the Marina Area last time in 2019, Chennaiyin FC had pocketed full points.
A brace from Pereyra Diaz and strikes from Lallianzuala Chhangte and Alberto Noguera sealed the win for the hosts while Iker Guarrotxena was on the scoresheet for the Gaurs.
Odisha FC has been irrepressible in the last two games emerging as the comeback masters. The Juggernauts left it late against Chennaiyin FC as they snatched all three points with a 95th-minute winner. In the game before that, they came from two goals down to win 4-2 against East Bengal FC. N
Pereyra Diaz's brace took him to the top of the league's goalscorers chart this season, while Lallianzuala Chhangte and Alberto Noguera also got on the scoresheet.