A draw suited neither side in this all-action game at Shamrock Rock.
Portadown remain just one from the bottom of the Carling Premiership table, with the Swifts one spot above them on goal difference.
The Ports, though, should have taken all three points, having scored a couple before the break and missed twice as many more chances as they carved holes in Dungannon’s rearguard.
“We made an absolute gift of a point to them,” said a furious Ports boss Ronnie McFall.
“We should have been out of sight by half-time. Not only did we miss a bagful, but we gave away two really soft goals. We need somebody to put the ball in the back of the net.”
Young Alan Teggart did just that after 18 minutes with Kevin Braniff — the mastermind behind most moves — running at the Swifts defence and slipping through a dream of a pass.
And it looked all over 10 minutes from the interval when Darren Kelly got onto the end of a peach of a free-kick by Ross Redman and the Ports were cruising.
But they paid dearly for those missed chances with Teggart, Wesley Boyle, Neil McCafferty and later Richard Lecky the main culprits.
The match turned on a rather bizarre goal just after the hour when Swifts star man Ryan McIlmoyle whipped in a cross from the left that went nowhere near a team-mate, but it dipped over the bemused David Miskelly into the net and the Tyrone-men were in business.
“Yes, I meant it as a cross,” McIlmoyle admitted. “But I’ve been instructed to get more balls into the box and it paid off.”
He also had a major say in the leveller five minute later when he sent a perfect corner onto Ryan O’Neill’s head and he bulleted it home, totally unmarked to claim a share of the spoils.