Dunne’s charges scored a three-point victory over the Tribesmen to set up a Leinster final clash with Kilkenny on July 13.
Dunne will hope his senior team can overcome Offaly in Saturday’s All-Ireland qualifier to cap a positive week for the Model County.
Jack Pettitt’s early goal proved the difference as Wexford avenged last year’s Leinster intermediate final defeat to Galway.
But it was an avoidable concession from a Galway viewpoint as Tommy Dwyer’s long free was batted away by goalkeeper Joe Keane and Pettitt reacted quickest to whip home the loose ball.
That score helped Wexford build up a comfortable lead midway through the first half as the Slaneysiders moved seven points clear, 1-7 to 0-3.
But a youthful Galway outfit dug in and had the gap back to three points on two occasions. Four unanswered points cut Wexford’s lead by the 19th minute and Galway were in touch at half-time, trailing
0-9 to 1-10. On a night when the Tribesmen registered 15 wides, they will have left O’Moore Park with a feeling of what might have been.
Wexford managed to keep Galway at arm’s length throughout the second half and while the margin was down to two points with five minutes remaining, Dunne’s men held out.
Galway lined out with seven U21 panellists in their starting team and two of the county’s 2015 All-Ireland minor winning side, including Seán Loftus, captain last September.
Brian Concannon and Jack Kenny came off the bench to swell the minor contingent but Wexford still managed to get the job done.
T Dwyer 0-6 (5f), J Pettitt 1-2, J Doyle 0-4 (1f), S Donohoe, B Dunne, G Moore, R Mahon 0-1 each.
A Helebert (3f) and N Morrissey (4f) 0-4 each, S Loftus 0-3, C Burke 0-2, R Lane, R Cummins, B Concannon 0-1 each.
D Hughes; A Maddock, Seán Murphy, S Donohue; J Kelly, R Kehoe, K Sheridan; B Dunne, T Dwyer; J Doyle, D Martin Carroll, J O’Connor; G Moore, J Pettitt, R Mahon.
Shane Murphy for O’Connor (39), J Firman for Moore (39), D Shanley for Shane Murphy (52), R Donohoe for Mahon (57), N Kirwan for Pettitt (57).
J Keane; V Doyle, B Flaherty, S Bannon; S Loftus, M Dolphin, S Roche; N Morrissey, A Morrissey; C Burke, A Helebert, R Lane; R Cummins, P Gordon, J Ryan.
R Bellew for Helebert (h.t.), B Concannon for Lane (42), J Kenny for Morrissey (42).
Gavin Quilty (Kilkenny)