Portadown firsts struggled on the road as Dromore’s determined display resulted in a 20-7 defeat.
An early penalty handed the hosts control before Portadown’s response placed Dromore on the backfoot.
However, a penalty miss within strong winds left the visitors without any reward.
A penalty try converted by Chris Cousens handed the away side a welcome end product before half-time.
The home side’s hard-working pack proved decisive late in the half to push Dromore clear by 10-7.
Dromore pushed on with the advantage of the second-half wind to score a converted try and penalty.
Portadown fourths and Larne will meet in a cup replay following last weekend’s draw.
Jamie Matthews proved in control from the outhalf position and the pack worked hard despite difficult weather conditions.
Captain Simon Lappin and his fourths must now line out against Larne in a cup replay.