The home side dominated the opening 45 minutes and thought they had opened the scoring midway through the first half when O'Neill finished coolly from a Chris Gallagher assist.
The referee's assistant had other ideas, however, and ruled the goal out for off-side.
Conor McKendry came closest to finding the net but was twice denied by smart saves from Portadown keeper Alex Moore, deputising for the suspended Aaron McCarey, and once by the outstretched leg of defender Divin Isamala.
The visitors had their moments, not least just before the break when striker Eamon Fyfe raced on to a Ben Quinn pass and forced Rohan Ferguson into a diving save high to his left.
However, the home side scored three times in a six-minute period to effectively kill off the game and preserve their unbeaten record on their home patch.
Randall scored the first of his two goals eight minutes after the restart with the midfielder curling his right-footed effort into the roof of the net.
Three minutes later he did it again, this time from slightly closer range, after Gary Thompson had committed a foul on the edge of the Portadown penalty area.
Visiting keeper Moore may have known what was coming, but he was powerless to prevent the same result.
The game was put to bed just before the hour when top scorer O'Connor notched his fifth of the season, racing clear of a tiring Portadown defence to plant a low shot past Moore.
