Colm Robinson and Liam Gervin combined to hit a total of 1-7 as the Barrys roared into the last eight. Moortown pulled a goal back through Peter Devlin, whose 20th minute point closed the gap to two points.
But Derrylaughan finished with a couple of excellent scores from Liam Gervin and Martin McStravog, while Moortown were reduced to 14 men when centre-back Damien Crozier was sent off.
The remaining three quarter-finals ended in draws, with Carrickmore’s 0-6 each stalemate with Clonoe the latest tie to require a replay. Tyrone star Conor Gormley thumped over a stoppage time leveller to earn Carmen a draw.