The game, which has been postponed no less than four times, finally got the go-ahead but there was no joy for Tim McCann's side, who remain eight points behind Donegal Celtic at the foot of the table.
For Portadown it was a big win and they showed they have not given up hope of a top six finish by improving their goal tally if that comes into play after Saturday's final round of games before the split.
Distillery's hopes took an early blow when the Ports took the lead after just six minutes. A deep free kick from Chris Casement was met by Darren Murray and his header went in off the base of the post with goalkeeper Lee Windrum stranded.
Windrum did much better a few minutes later when he made a double save to deny Murray and Mark Patton with the follow up.
The Ports were by far the most creative and it was no surprise when they doubled their lead at 31 minutes. It came from the left flank as Mark Patton skipped past defender Garrett, and his cross was drilled home by Murray from close range.
In the next attack Kevin Braniff connected from 20 yards out but his firmly struck shot was well saved by the home keeper.
The Whites made a triple substitution at the start of the second half, but they were soon 3-0 down as Murray notched up his hat-trick at 51 minutes.
The Ports striker brought the ball down in the box, rolled defender Simpson and struck a firm shot which took a deflection off Hunter and past Windrum to record his 15th league goal of the season.
Another sweeping move brought a fourth goal for the visitors with Patton pulling the ball back from the by-line for Sean Mackle to tap home.
Ports keeper David Miskelly was rarely called into the action but he did very well to push away a superb long range effort from Melly.
Braniff made it 5-0 with another close range finish after good work by Mackle. Braniff had a chance to make it six from the penalty spot after Hunter handled in the box, but he smashed the spot kick off the bar.