Joe pulls the plug on battling Suds.
A shock was on the cards when Christian McClean gave Sudbury the lead midway through the first half.
That left Second Division leaders Brentford facing Cup oblivion.
But it all went sour on Sudbury when Brentford put on muscular sub Joe Omigie at the start of the second half.
He had too much pace and power for a tiring defence and had a hand in all three Brentford goals.
And Sudbury manager Richie Powling admitted that the better side had won.
"Teams at our level aim at getting to the first round of this competition - we went one better and fell to the best team left in it," he said.
"My lads gave all they had. They have nothing to be ashamed of and I'm proud of every one of them."
Sudbury went out with their heads held high. Even when Brentford were giving them a chasing they refused to throw in the towel.
Brentford's extra class had Sudbury at full stretch from the start.
But the Bees got a shock when the non-Leaguers swept ahead in the 23rd minute.
McClean rose highest in a packed goalmouth to get the finishing touch after Gus Hurdle headed a corner from Sudbury skipper Nicky Smith across his own goal.
Sudbury then dug in and battled away to protect their lead until the interval.
But Omigie made his mark in the first minute of the second half - a clattering into Sudbury keeper Steve Mokler.
Bees' David McGhee levelled in the 51st minute.
He netted from close range after Carl Asaba played the ball in and Omigie unsettled the defence to set up the chance.
Seven minutes later Robert Taylor fired Brentford ahead after Omigie split the Sudbury defence.
And Taylor got the third in the 74th minute after Jason Carter and Tony English got in a tangle to leave him free.
Only the gallant Mokler prevented Sudbury losing by a bigger margin.
He had no chance with any of the goals that beat him and produced a string of outstanding saves.
But he injured a shoulder when he crashed into an upright - an injury that needed heavy strapping at half-time.