Thomas Frank made eight changes to the team that had been beaten by Manchester City in the Premier League on Saturday and the gamble looked at risk of backfiring when defender Brandon Cooper stunned home supporters in west London with an early tap-in to hand Richie Wellens' side the lead.
But Frank's stand-ins rallied and replied with three goals before the break, the highlight a fabulous overhead kick from Carvalho to equalise, before Mikkel Damsgaard's header and Christian Norgaard's 18-yard strike established a two-goal lead.
Orient stayed in the game for much of the second half until captain Jack Simpson was sent off 20 minutes from time, as a brave display ended in a cup exit.
The team currently 22nd in the third tier began boldly, defying their lowly league placing. Inside the opening 10 minutes, impressive Tottenham loanee Jamie Donley carried the ball infield from the right, bounced an attempted through ball off Ben Mee and, as it broke back to him, hit a shot that deflected wide off Norgaard.
The opening goal moments later was no more than Orient's early ambition deserved. Winger Diallang Jaiyesimi showed fleetness of foot to make space to shoot, hitting an effort that spun away to the right-back Tom James positioned near the touchline. He sent over a wicked cross that was side-footed in unmarked at the far post by Cooper.
The equaliser was not long in arriving. A superb run by Kevin Shade ended in him dispatching a low shot that pinged into the air off the foot of goalkeeper Josh Keeley. From the rebound, Carvalho leapt acrobatically to crash an overhead kick inside the post for his first goal since joining from Liverpool.
Damsgaard completed the turnaround after 26 minutes and this time Carvalho was the provider, whipping a fine ball to the far post that was finished with a clever diving header by the Denmark winger.
His countryman Norgaard rifled in the third before half-time. Carvalho tumbled over the leg of Orient's Dom Ball on the edge of the box and, before the referee was called to make a decision over whether to award a penalty, Norgaard had aimed a devilish first-time effort into the far corner to make it 3-1.
Substitute Charlie Kelman ought to have brought Orient back into it on the hour mark but failed to squeeze his shot inside Hakon Valdimarsson's near post after going clean through.
Mads Roerslev cracked a shot into the side-netting from 20 yards as Brentford sought to kill the game, before Orient's fate was effectively sealed with Simpson's sending off, shown a second yellow card for a needless rugby tackle inside his own half on Shade.
