Jeje slammed the ball home past a hapless Gurpreet after the ball deflected off the BFC defender just five minutes into the match.
Bengaluru skipper Sunil Chhetri equalised for the hosts in the 85th minute but in 88th minute Ganesh sealed the hosts' fate with a brilliant header off Rene Mihelic floater.
With this loss, Bengaluru are relegated to second position on the points-table with 12 points of six games. Chennaiyin garnered three points and are placed third with FC Pune taking the fourth position with nine points in six games.
In 86th minute, Chhetri was furious over poor officiating by Rakitm Saha who did not award a free-kick to him after being brought down by Henrique Sereno on the run.
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Bengaluru looked a shadow of their usual self in the game which witnessed more dramatics, fouls and rough tackles than football.
Goal-scorer Ganesh was handed a yellow card after a major scuffle in the pitch. Chennaiyin players were angry over not getting the ball back when the play resumed after Sereno's injury.
Chennaiyin were unlucky in 22nd minute to be awarded a penalty after referee Raktim Saha failed to notice Khabra knocking down Jeje with his elbow as he leapt on top of him to shield the incoming ball inside the box.
Chennaiyin could have romped home the second goal, but due to Jude's slackening run into the box gave ample time for Khabra to clear the ball to safety of a well-timed tackle.
The hosts had their chance in the 40th minute after Chhetri seized on to a rare defensive lapse by Chennaiyin, but could not capitalise on it as the shot went meters wide off the target.
The hosts had their best chance to send in an equaliser through Chhetri, but his first time shot was too weak to trouble any Chennaiyin defender, in 46th minute.