The match ended goalless at regulation time.
While the Bengaluru team converted all the penalties, Chennai FC missed one to bow out of the tournament.
For ASC, the scorers were: Thiygarajan, Thirunavakarasu, Neeraj, Arunjit and Jerin.
John Peter, Sanjay Sharma, Swanta Mistri and Gudipath Kumar found the net for the city club.
ASC takes on Goa FC in the final, tomorrow.