Danny Purkis' solitary goal right on half-time proved enough for Gary Hamilton's Glenavon to extend their unbeaten run to five games and stay in the top-six mix in a reasonably lively encounter at a bitterly cold Mourneview.
Purkis almost opened the scoring as early as the second minute when he got a touch on Matthew Fitzpatrick's right-wing cross but directed it just wide. The striker then forced Point keeper Gabriel Sava into a smart stop at his near post with a rasping drive just three minutes later.
Glenavon broke the deadlock in the final minute of normal time in the first half with an opportunist goal from Purkis, who had looked the most likely to score in the opening 45 minutes.
The goal came from a mistake by the usually reliable Colm Deasy. His back-pass to Sava was much too short and that allowed Purkis to nip in ahead of the keeper on the edge of the box, round him and slot home from the left-hand side to give the hosts a lead they just about deserved at the break.
It should have been two on 56 minutes with Greg Moorhouse left wondering how he didn't find the net with two chances in as many seconds.
The first was a header from a Robert Garrett corner that Sava superbly tipped onto the bar and when the ball rebounded out to Moorhouse six yards out, the striker blasted wildly over.
Sava then got down low to hold onto an Aaron Harmon snapshot three minutes later as the hosts looked to turn the screw and turn their dominance into goals.
Insult to injury was added for Warrenpoint at the death when Dermot McVeigh was harshly shown a straight red card by referee Evan Boyce for bringing down James Singleton as the hosts broke on goal.
Glenavon: Hyland, Douglas, Harmon, Ward, Singleton, Garrett, Snoddy, Moorhouse, Fitzpatrick (McCaffrey 81), Purkis, Campbell (O'Connor 57)
Subs not used: J Taylor, Norton, J Doyle, O Taylor
Warrenpoint Town: Sava, Deasy, Ball, McVeigh, Byrne, Gallagher, Hutchinson (Carroll 81), Dillon, Evans (Swan 86), O'Sullivan, Doyle
Subs not used: Sava, McCaffrey, Mullen, Cowan, Wallace
Referee: Evan Boyce (Ballygowan)
Man of the Match: Gabriel Sava (Warrenpoin)
Match Rating: 6/10