Chhetri scored in the 13th, 55th and 90+4 minutes while Pritam Singh (45+3) pulled one back for Neroca.
Bengaluru FC, the losing finalists of the ISL, now face I-League side Mohun Bagan in the semifinal on April 17.
Bengaluru were soon rewarded for their consistent attacks in the 13th minute through a cross from the left flank from Udanta Singh that was duly punched out by Neroca goalie Lalit Thapa but Chhetri was there to nod the ball home with a spectacular header.
Neroca struck back with an equalizer in the stoppage time of first half, when a silly mistake from Gurpreet Singh of not collecting the ball properly saw Pritam Singh (45+3) making no mistakes in finding the net.
Neroca had sealed their quarterfinal spot by defeating Kerala Blasters after coming from behind but they could not really repeat the feat today. Their hopes were dashed in the dying moments of the match when Chhetri struck his third goal of the game.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)