The winger’s spot kick cancelled out a stunning strike from Kevin Monzialo but neither side was able to edge in front.
It was Brentford who would have the first chance of the afternoon when Fredrik Hammar tried his luck, but despite finding himself in a bit of space, he fired over.
It would be the away side who would find the net first, though, and they did it in style when Monzialo was afforded room before unleashing a vicious effort which beat Patrik Gunnarsson in the Brentford goal from the edge of the box.
Brissett would then have his first attempt just moments later when he darted down the right before cutting inside and shooting powerfully, but for a save by Marvin Keller in the Zürich goal.
Brentford would be given a penalty just after the half hour mark when Hammar got inside the area before finding space and shooting, but for a stray hand which saw the Zürich defender block the shot and the referee immediately pointed to the spot.
Brissett would then step up to convert the penalty to make it 11 Brentford B goals for the season as he slotted the ball into the right-hand corner.
Cole Dasilva and Hammar would have more shots towards goal before the break but neither were able to find the net.
Fabio Fehr would have two quickfire attempts after the break, the first of which was well saved by Gunnarsson before his second shot was side footed just wide of the post following good play down the left.
Just after the hour mark the away side went inches from going back ahead when Max Mata controlled fantastically before he curled an effort towards the top corner but for the post as The Bees managed to clear the rebound.
The two Brentford full backs in Tom Field and Dasilva would also go close for the home side, but for the former to have his driven shot blocked and Dasilva’s low effort whistled just wide of goal.
A couple of late Kane O’Connor clearances would be the end of the action as the match finished even.
Brentford B: Gunnarsson, Field, Mitchell, O’Connor, Koutsimouka, C. Dasilva, Brissett (Adams, 63), Coote (Oksanen, 55), Hammar, Trialist (Trialist, 45), Majka Subs not used: Tsaroulla, Andersson, Titov, MogensenBooked: Mitchell
Grasshopper Club Zürich: Keller, Dickenmann, Pinjaker, Mesonero, Scheidegger, Monzialo, Mata, Schneider, Fehr, Moke, VukelicSubs: Hoxha, Tschopp, Hadorn, Bahtiyari, SchiesserBooked: Monzialo