It was tight for most of this game but a converted try close to time made the scoreline look as though the Ballymoney team were much more dominant.
After 15 minutes, they took the lead with a try by loose head prop Aaron Christie try but the visitors were ahead by half-time when, following a box kick, out-half Kyle Beattie scoring and added the points.
At the start of the second half Dalriada managed to regain the advantage.
Matthew Lockhart went over for their second and then out-half Angus Johnston also crossed for both to be converted by Stewart Moore to leave the Ballymoney school 19-7 in front.
Dalriada's final try came after an Omagh error and a number of pick-ups with Thomas Hunter the scorer for Moore to goal.
Omagh, who had to make a late replacement for out-half Neil Logan after he had an appendectomy on Friday, kept attacking whenever possible and his replacement Glen McKinley ended off a move that involved James Longwell for Beattie to add the points.
Home coach Rab Gregg thought his team played hard and reorganised well after the yellow card was shown twice just before half-time. "It was tight until we scored our final try and Omagh gave us a tough challenge," he said.
Omagh coach Ross Hunter felt his team left a lot of points on the pitch. "Both teams defended well although Dalriada were slightly better. Our backs did well to stop their hard running players in their tracks. All in all they took their chances and that's what it's all about."
Dalriada now have the difficult task of travelling to Foyle College to face a team with two convincing cup wins behind them.