A first-half goal from Marcus Kane gave Glentoran a deserved victory over Portadown, who had Keith O'Hara sent-off for a foul in the final minute.
Kane struck a right-foot effort past Billy Brennan from the edge of the box.
O'Hara was dismissed for bringing down Steven Gordon as he raced through on goal, while unused substitute Mark McAllister was red-carded for dissent.
In the first half, Allen's attempted lob went wide of the post, while Darren Murray fired wide at the other end.
Gordon also went close for the hosts against the strangely subdued visitors.
The Glens move into sixth in the table, ahead of the Ports on goal difference.
Glentoran manager Eddie Patterson: "We weren't happy with the attitude last week so we worked on a few things in training and made a few changes to the team.
"We played some fantastic stuff in the first half and we had to dig deep and defend in the second. It was a deserved three points."