Orient went ahead through Brandon Cooper before Carvalho and Mikkel Damsgaard struck their first goals for the Bees and Christian Nørgaard took the game to 3-1 before halftime.
Jack Simpson was sent off for Orient for two bookable offences.
Afterwards, Brentford boss Thomas Frank said: “It’s job done. I’ve said it many times: we want to go on a cup run, we want to go as far as possible and potentially win it - we know it’s difficult but that’s the aim.
“In these games, I need to find the perfect balance between putting a strong team out there, the mix of freshness but also with the game on Saturday in mind, and then also using the squad, because players need that to develop and also want to be included.
“We hit the level today; credit to Leyton Orient, they did well in the first 20 minutes, we didn’t get enough control, but then we got our goal, and from there we were in control.
“3-1 ahead at half-time; second half, I wanted us to be even more on top, but it’s not easy, they gave everything. But I'm pleased."