Portadown had two goals in the closing 15 minutes to thank for safe passage past Portstewart.
The Irish Cup trip handed Ronnie McFall’s men a test against a side in the third tier of the domestic game.
Clear sights of goal proved few and far between but Portadown eventually gained control thanks to goals by Gary Twigg and Darren Murray.
Twigg managed to break the deadlock at the second attempt after a cross into the box by substitute Sean Mackle.
Portstewart’s Joel Maddison managed to block the initial attempt by Twigg but the ace striker made no mistake off the rebound.
Murray closed out the scoring by reacting first to convert after Maddison struggled to hold Tim Mouncey’s long-range drive.
Mouncey was at the heart of the limited first-half action and attacked on two occasions a dangerous free-kick by 18-year-old Jake Richardson.
Peter McMahon had a shot blocked before the break after good work by Ross Redman along the left.
Mistakes by Redman and Garry Breen offered Portstewart hope of a cup shock as the sides entered the break on level terms.
Clever play from Robert Garrett resulted in a snapshot by Murray that flashed the wrong side of the post.
Murray almost capped neat footwork by Shea Conaty with a strike on target but his drive cleared the crossbar.
Maddison produced a superb point-blank save to frustrate Murray off a Mouncey header.
McMahon also fired wide as the Ports pushed for the upper hand.
PORTSTEWART: Joel Maddison, Luke Bradley, Ryan Campbell, James Peden, John Neill, Stuart Millar, Lee Forgrave, Richard Vauls, Nigel Turner, Johnny Stewart, Ryan Doherty. Subs: Dean Murray (on for Millar, 91 mins), Robert Donnel (on for Stewart, 74 mins), Craig Ramsey, Davy McClements (on for Turner, 83 mins), Ryan McCallister.
PORTADOWN: David Miskelly, Ross Redman, Keith O’Hara, Garry Breen, Peter McMahon, Darren Murray, Tim Mouncey, Gary Twigg, Shea Conaty, Robert Garrett, Jake Richardson. Subs: Billy Brennan, Sean Mackle (on for Conaty, 65 mins), Paul McElroy, Jordan Lyttle, Marcio Soares (on for Twigg, 84 mins).