Byrne’s eighth goal of the season - his fourth in five games - settled a nondescript affair as Wexford, who deserved a point, wasted an opportunity to make up ground on Finn Harps.
Shane Keegan’s side, four points behind Harps in the relegation play-off place, remain six points ahead of bottom side Longford Town, though now with the same number of games played.
Despite six changes from Friday’s 0-0 draw with Derry City, Wexford started the better with Bohs’ Shane Supple the first keeper worked on 21 minutes, getting across well to save Aidan Friel’s left-foot drive from distance following a weak clearance by Paddy Kavanagh.
The home side gradually settled and troubled Graham Doyle in the Youths goal for the first time four minutes later. Keith Buckley arced a cross in from the right with Doyle going full stretch to clasp Byrne’s glancing header.
Much of the action was at the other end, though, with the influential Molloy volleying wide across goal after a free kick from Shane Dunne dropped to him. Then, somewhat against the run of play in the final minute of the half, Bohemians took the lead.
Byrne’s initial header from Kavangah’s cross was touched into the air by the off balance Doyle before the striker followed up to poke the ball over the line.
Lax defending might have cost Youths a second goal eight minutes into the second half when Derek Prendergast was allowed get his head to a Lorcan Fitzgerald cross to flick the ball just over the top.
Keith Buckley then threaded a delightful pass through for Byrne who saw his shot trickle wide across the face of the Youths’ goal.
Supple; Pender, Prendergast, Morris, Fitzgerald; P. Kavanagh (Kelly, 70), Lopes, Wearen, O’Halloran (Quigley, 70); Buckley; K. Byrne (D. Byrne 90+3).
Doyle; Friel (Murphy, 82), Grace, Last, O’Connor; Molloy, Higgins, Kenny, Dunne (Mulligan, 72); Furlong, Porter (Keenan, 61).
Dave McKeon (Dublin).