Callum Wilson found the net for the first time in a Brentford shirt as the club secured passage into the next stage of the Carabao Cup with a dominant display.
The west London outfit, who had impressed greatly in their Premier League victory over Tottenham at the weekend, fielded a altered starting XI and showcased the strength of their resources with a polished performance under Keith Andrews.
Wilson opened the scoring early on and, after Demarai Grays reply, two goals in the space of five minutes towards the end of the opening period gave the travelling side control, with Aaron Hickey and then Nathan Collins both on target.
Three goals inside seven minutes after the break completed a comprehensive win, with Mikkel Damsgaard, Collins again, and Igor Thiago all scoring.
New summer recruit Wilson was supplied by Yehor Yarmolyuk and the forwards effort found the net with assistance from a deflection off Birmingham defender Dael Fry.
The second-tier club drew level when Gray struck the ball firmly into the net, but Brentford were throughout the superior team and responded when Hickey swept the ball into the far corner after Birmingham failed to deal with the situation, before Collins met Jaidon Anthony’s delivery with a headed finish.
Anthony also played a role in the fourth and fifth goals, with Thiago cleverly allowing his cross to continue to Damsgaard, who finished with conviction, before Anthony cut the ball back for Thiago to convert.
Collins glanced a looping header from Mamadou Sangares pinpoint cross to make it six goals.
Brentford: Valdimarsson; Hickey, Collins, Schuster, Henry; Janelt (Kayode 71), Yarmoliuk (Sangare 48), Damsgaard; Ouattara (Schade 46), Wilson (Thiago 62), Anthony Subs not used: Kelleher, Ajer, Lewis-Potter, Jensen, Carvalho.