The Nomads ended a run of six games without a win to leave Prestatyn still dangerously close to the relegation zone.
Nomads took a seventh-minute lead when Danny Forde was given space and time to chest the ball down and fire past keeper Jon Dunt.
Steve Bowes went close to levelling matters with a 20-yarder that hit the woodwork, but Ian Griffiths got the equaliser on 22 minutes, holding off defender Teddy Whelan to volley over keeper Terry McCormick from 25 yards.
Phil Doran hit a post for Nomads, but Prestatyn almost took the lead when Griffiths' shot was just kept out by McCormick, who then produced a superb stop from Jon Fisher-Cooke.
Quay spurned a chance to take the lead just after the hour when Liam Loughlin's penalty was saved by Dunt after Ronnie Morgan's cross had been handled by David Hayes.
But Phil Doran eventually nudged the hosts in front with a shot on the turn and Morgan had better luck from the spot seven minutes from time after a foul by Danny Dustain, who was red-carded.
Stats and report courtesy of welsh-premier.com