Barnet clung on to remain deadlocked on 90 minutes thanks to goalkeeper Brill’s three superb saves, but he was not called upon during penalties as Jonathan Douglas fired over and Danny Senda netted the winner.
Brentford started brightly and should have taken the lead after four minutes when Michael Hector slipped and Niall McGinn lobbed against the bar.
Brill was called into action for the first time 10 minutes after the restart, superbly denying Marcus Bean’s point-blank header and Toumani Diagouraga’s follow up.
The hosts threatened on the hour as Mark Marshall left two defenders in his wake, but could not find the target from distance.
Clayton Donaldson then beat the offside trap, though he was only able to find the grateful arms of Brill with the goal at his mercy. And Brill earned Barnet the shootout, beating away Harlee Dean’s late strike, before his team-mates held their nerve, converting all five kicks, to set up a two-legged area final with Swindon.