The O's took the lead in the first half when top scorer Josh Williams hit his fourth goal of the season. Portishead equalised shortly afterwards but Jack Parker made it 2-1 early in the second half.
O's thought they had stretched their lead when Jordan Greenwood's header was saved by the keeper then bundled over the line by an Oldland boot in a melee but the "goal" wasn't given. Both sides had opportunities to score late on but the O's held on and now sit handily just two points off fifth place.
On Saturday, Oldland make their longest trip of the season when they entertain second placed, free scoring Barnstaple Town.