Brentford twice fought back before beating Premier League West Brom 5-4 on penalties in the Carabao Cup.
All four goals in normal time came in the second half, with Hal Robson-Kanu putting the hosts 1-0 and 2-1 in front from the spot.
But Emiliano Marcondes' superb overhead kick and a Marcus Forss spot-kick drew the Bees level to force the shootout.
Christian Norgaard scored the winning penalty after Grady Diangana's effort had been saved.
Brentford will host Premier League Fulham or Championship rivals Sheffield Wednesday in the fourth round. The Bees have never progressed beyond the fourth round of this competition in their history.