Kyle Wyatt fired The Reds in front after 21minutes after he had been played clear through.
And substitute Liam Ormsby sealed the win on 86minutes when he fired home from 18yards.
The Reds now face the Derby County Academy in the Fourth Round.
BARNSLEY: Waggett, Smith (Devonshire 88), Potter, Jennings, Waterfall, White, Frost (McGrory 86), Butterfield, Brown, Wyatt (Ormsby 68), Fedorenko.
Subs: Simmonds, Free.
LEYTON ORIENT: Jennings, Matthews, Kemp, Shields, O'Donnell, Webb, Martin (Atu 56), Page, Pires, Bolle, Grange (Russ 86).
Subs: Doyle, Sydes.