Portadown remain four points behind Premiership pacesetters Linfield thanks to a 2-0 win at New Grosvenor.
Ronnie McFall's men took the lead in the 22nd minute when Jamie Tomelty's corner from the left was headed in at the back post by defender Gary Breen.
For Distillery, Neal Gawley was just wide with an ambitious overhead kick.
The Ports wrapped up the points seven minutes from time when a driven cross by Andrew Burns was deflected in by Philip Simpson for an own goal.
That made sure of Portadown's fourth successive win over Lisburn Distillery.
Early in the second half, with the Ports 1-0 up, Matthew Tipton had a chance to score but Billy Brennan made the save.
At the other end, a David Cushley effort was pushed around a post by visiting keeper David Miskelly.