Portadown moved above Crusaders into third place in the Premiership thanks to Sean Mackle's spectacular second-half shot off the underside of the bar.
In the first half, Darren Murray almost squeezed the ball under Aaron Shanahan while Emmett Friars twice headed over from Chris Casement corners.
The strong wind and rain hampered the quality of the play throughout but the visitors almost equalised late on.
Michael McLellan had the ball in the net but the flag was up for offside.
The result extends the Ports' unbeaten home league record to eight games and they must now wait two weeks for their next fixture, against mid-Ulster rivals Glenavon.
Sixth-placed United host in-form Cliftonville at the Showgrounds on Tuesday night.