Bohemians will take a one-goal lead into the second leg of their Setanta Sports Cup first round tie against Portadown next Monday night.
Dinny Corcoran put Bohs in front with a delicate chip over David Miskelly from outside the area in the 44th minute.
Karl Moore added the second with a stunning left-foot shot into the top corner of the net on 57 minutes.
Kevin Braniff headed in from close range after Brian Gartland flicked on a throw-in after 60 minutes.
Ross Redman had the first chance of the game for the visitors but his left-foot shot was saved by Craig Sexton.
After Corcoran's opener, Keith Ward shot just wide and Cororan went close with a left-foot shot from a narrow angle.
With the score at 2-1, Braniff headed just over.
Ports manager Ronnie McFall will be concerned by a calf strain sustained by striker Matthew Tipton ahead of Saturday's big Irish Premiership game against Linfield.