The player manager brought the sides level in the second half and Guy Bates added the second goal to give the Lurgan Blues three points and move them two ahead of Ballymena into sixth spot in the table.
Earlier the visitors had made a bright start, but it was Warrenpoint who forged ahead on 20 minutes. Daniel Hughes, a target for Glenavon in the transfer window, raced clear after being put clear by brother Stephen and he directed his shot past James McGrath in the Glenavon goal.
David Rainey had a great chance to level matters soon after but unmarked, he put his header wide from a flick on by Murphy.
Warrenpoint maintained their one goal advantage at the break but Glenavon hit back in the second half.
Gary Hamilton came off the bench to replace Rainey and within minutes had the ball in the net. The home team failed to clear the ball and Hamilton nipped in to beat Hughes in goal with his firmly struck shot.
Another second half sub Andy McGrory went close with a shot which shaved the bar while Hughes almost grabbed his second of the night when lining up his shot but he hit the side netting.
The comeback was complete on 78 minutes and it was a rather lucky break for Guy Bates. Goalkeeper Hughes slipped going to collect a back pass and Bates nipped in to rob him and the ball was eventually forced over the line.
James McGrath insured Glenvaon left Dungannon with all three points making a fine save to deny Bagnell.
Warrenpoint Town: B Hughes, King, Cowan, Moan, Boyle (Devlin 85), Stephen McCabe, Bagnall, M Hughes, S Hughes, D Hughes, S Parr. Subs not used: Kearns, Smith, Grant, Havern
Glenavon: McGrath, Singleton (Patton 79), Murphy, McCallion,McKeown, Neill, Kilmartin, Martyn, McCaul (McGrory 53), Rainey (Hamilton 53),. Bates. Subs not used: Shane McCabe, Mulvenna