The Bees were value for the win, with Samman Ghoddos having hit the bar and Sergi Canos missed a sitter before Dasilva’s 66th-minute strike settled the tie and sent the Bees into the semi-final of a major cup competition for the first time ever.
Newcastle became the fourth Premier League side to have been knocked out of the competition by Thomas Frank’s side this season, joining West Brom, Fulham and Southampton.
Thomas Frank took a risk by staying loyal to many of the squad players who had starred in the early rounds, leaving topscorer Ivan Toney on the bench as he made six changes to the side that had beaten Reading in the Championship at the weekend.
Callum Wilson forced Luke Daniels into a smart save, before Ghoddos skewed down into the pitch and up onto the crossbar when he should have done better with Dasilva’s cut-back.
Canos was then guilty of wasting the first half’s best chance, somehow heading wide from six yards at the end of a clever corner routine.
The breakthrough came midway through the second half, when Canos made amends for the miss with a lovely pick-out of Dasilva, who sidefooted home on the volley to give Brentford a lead they never looked likely to surrender, even as Steve Bruce through caution to the wind with the introductions of Dwight Gayle, Joelinton and Andy Carroll.
In fact, it was the Bees who went closest to adding to the score, substitute Toney denied by a smart low save from Karl Darlow in stoppage time.