It was Lurgan who opened the scoring when Scott Wilson kicked an early penalty, but Dungannon responded immediately with a try from loosehead prop Jonny Black. Captain John Buckley was on target with the conversion for a 7-3 lead.
Dungannon looked to be the stronger side and Matthew Clarke capitalised on pressure to grab a well-worked try, giving his team a 12-3 advantage going into half time.
Black got his second score of the game just after the break and Buckley added the extras to push the scoreboard to 19-3.
The boys from Lurgan College showed great heart to fight their way back into the game and were rewarded when Jonny Hunter intercepted a loose pass and raced clear to score under the posts. Robbie Norton had the simple task of converting from straight in front and that reduced the deficit to 19-10.
But there was still time for Dungannon to register two more tries, through number 8 Pete Doran and fullback Aaaron McCammon.