After a goalless first half, Jerin opened the scoring with a strike in the 49th minute to put ASC ahead.
Nine minutes later, Dawa beat the DBYC goalkeeper to put the team 2-0 in front.
Jerin scored again in the 85th minute to end the host team's stay in the competition.
ASC will take on Hyderabad TFA in the last eight.
Bengaluru DFA meets Chennaiyin FC 'B' in tomorrow's quarterfinal.