Marcello Trotta's stunning strike moved Brentford into third place as Crewe came back down to earth with a bump following Sunday's Wembley triumph with a 2-0 home defeat.
The Fulham loanee scored two minutes after coming on as a substitute to put the game beyond doubt after Bradley-Wright-Phillips had headed the visitors in front with 12 minutes gone.
Shaleum Logan ran onto Clayton Donaldson's back-heel before crossing for Wright-Phillips to bury a near-post bullet header past keeper Steve Phillips.
Things got worse for the home side when Phillips took a whack in a challenge with Tom Adeyemi and had to be replaced by Alan Martin.
Bees defender Harlee Dean cracked a header off the crossbar and Donaldson went close from the rebound with a overhead kick before Martin kept out another Wright-Phillips effort.
Matt Tootle shot from the edge of the box in a rare attack for Crewe, who won the Johnstone's Paint Trophy three days earlier, but keeper Simon Moore tipped the ball to safety.
Logan appeared to handle Byron Moore's cross only for referee Robert Madley to wave away their claims.
The Bees continued to boss the game after the break and Donaldson could have had a hat-trick after firing two free headers over the bar and seeing a shot saved by Martin after racing clear of the Crewe defence.
Douglas shot over before substitute Trotta put the game beyond doubt in the 84th minute with a stunning volley from 15 yards.