John Menoyngar put the I-League leaders ahead in the 21st minute lead before Joshimar d'Silva Martins' twin-goal blitz (45+1st and 57th) looked to snap their three-match winning streak.
But Chhetri's sparks of brilliance with goals in the 48th and 71st minute ensured that the Bengaluru juggernaut rolled on for their fourth successive victory.
This was Chhetri's third brace in as many games to take his tally to eight, one behind Joshimar jumped to lead with nine goals after today's effort.
Liberian recruit Menoyngar executed a Beingaichho Beikhokhei corner kick to perfection with a low left footer to give the visitors the lead after a couple of failed attempts from Mohammedan Sporting.
There was no lack of intensity from Mohammedan Sporting who made a comeback at the stroke of half-time with a rare midfield and goalkeeping error by Bengaluru FC.
A long ball played out by Colin Abranches was taken in control by Joshimar who shot it into the target with a goalkeeping lapse by Pawan Kumar.
But Mohammedan Sporting once again held Bengaluru's surge with Joshimar striking from a rebound that came from Pawan Kumar.
Chhetri sealed the issue with a brilliant header that came off another Thoi Singh corner.
It was a heart break for Mohammedan Sporting who started out aggressively and could have awarded a penalty after Orji Penn was brought down by Curtis Osano in the 12th minute, but the referee Ratheesh Kumar thought otherwise.
Playing with only Joshimar in front, Mohammedan Sporting clearly missed the Aussie Tolgay Ozbey who is nursing an injury.