Bray’s deserved win, their first since beating Shelbourne on the opening night, ended a run of seven straight defeats and lifts them off the foot of the table above now second-bottom Shels.
Shelbourne fans once again voiced their disapproval afterwards, calling on manager Alan Mathews to go.
The first chance came to Shelbourne less than 90 seconds in when Mark Leech was in one-on-one with Darren Quigley, who saved well with his feet, though the striker should have scored.
Three minutes later Jason Byrne got free behind the square Shelbourne defence, succeeding only to toe his effort fractionally wide of Ger Hanley’s right-hand post.
The home side took the lead on 19 minutes when Gary Dempsey threaded a ball through for Marty Waters, who held off the challenge of Brian Shortall to shoot past the advancing Hanley.
The goal just about summed up Shelbourne’s sluggish first-half display in what was a dreadfully poor spectacle.
Try as they might to apply some necessary impetus to their game on the resumption, Shelbourne continued to struggle and only a superb reaction save from Hanley, in tipping over from Ismahil Akinade, prevented Bray doubling their lead on 52 minutes.
Three minutes later though, Shelbourne punished sloppy defending to level.
Shane O’Connor’s attempted clearance merely succeeded in putting the ball into the air for Leech to score with a well-placed looping header over the poorly positioned Quigley.
However, Akinade had made a difference and his crossfield ball fed Mulroy on the right on 75 minutes to score what proved the winner. The winger still had plenty to do and he cut in onto his left foot and drilled the ball to the bottom corner of the net.
Shelbourne almost snatched an equaliser in stoppage time, but Quigley was equal to Leech’s overhead kick, touching it over the bar.
SHELBOURNE: Hanley; Flynn, Shortall, Ryan, Memery; Brennan (Hughes 33), Crowley, Hurley, Hanlon (Prizeman 52); Leech, Mooney (Kelly 76).
BRAY WANDERERS: Quigley; Hyland (Doyle 70), Webster, S O’Connor, Earley; Mulroy, Dempsey, Zambra, Knight (Akinade 46); Waters; Byrne (Joyce 83).
Referee: Rob Rogers (Dublin).