Galway 0-29 Wexford 1-17
Joe Canning and Conor Cooney weighed in with 0-18 between them at Croke Park as Galway came good with a storming second-half performance to claim the Leinster SHC title.
Micheal Donoghue's All-Ireland favourites and Allianz league winners played out a tense first half hour or so with Davy Fitzgerald's Wexford, the breakthrough team of the season so far.
Wexford led by 0-11 to 0-10 with 30 minutes on the clock but were burned off from there by a Galway side that opened up with some terrific hurling.
From that 30th minute until full-time, Galway outscored Wexford by 0-19 to 1-6 and simply had too much power, pace and attacking ability for the Model men after the break in particular.
Galway led 0-14 to 0-11 at half-time as they chased just their second provincial title and reeled off seven points in a row in the third quarter of the game to put themselves in a winning position.
It was a stunning display of aerial ability at that stage with Niall Burke, Joseph Cooney and Conor Cooney all winning balls in the air before dispatching them over the Wexford bar.
Nothing went right for Wexford in the second-half. They had a Conor McDonald point ruled out by Hawk-Eye shortly after the resumption despite being initially awarded by the umpire.
McDonald then had a penalty attempt turned around the posts by Galway 'keeper Colm Callanan.
Wexford did manage to halt Galway's momentum briefly with a 53rd minute goal from Diarmuid O'Keeffe who picked off 1-1 in total.
But Galway's response was emphatic as they hit back with five more points in a row including a converted sideline from Canning who appeared to hobble off late on when he was replaced by Shane Maloney.
Maloney and fellow substitute Thomas Monaghan both got on the score-sheet as the Tribesmen powered through to the All-Ireland semi-finals on the first weekend of August.
Wexford, who took out Kilkenny in the Leinster semi-finals, still aren't out of the All-Ireland race. They will travel to the redeveloped Pairc Ui Chaoimh later this month for the quarter-finals.
Scorers for Galway: J Canning 0-10 (0-8f, 0-1 65, 0-1 s/l), C Cooney 0-8 (0-01f), J Cooney 0-5, N Burke 0-2, P Mannion, D Burke, S Maloney, T Monaghan 0-1.
Scorers for Wexford: C McDonald 0-5 (0-3f), D O'Keeffe 1-1, L Chin 0-4 (0-2f, 1 65), P Morris, M O'Hanlon 0-2, J O'Connor, W Devereux, C Dunbar 0-1.
GALWAY: C Callanan; A Tuohy, D Burke, A Harte; P Mannion, G McInerney, J Hanbury; J Coen, D Burke; J Cooney, J Canning, J Flynn; C Whelan, C Cooney, N Burke
Subs: T Monaghan for Flynn (31), S Maloney for Canning 67, G Lally for J Cooney 68, S Loftus for P Mannion (72).
WEXFORD: M Fanning; L Ryan, W Devereux, J Breen; S Donohoe, M O'Hanlon, D O'Keeffe; L Chin, J O'Connor; P Morris, A Nolan, C McDonald; S M, J Guiney, H Kehoe.
Subs: D Redmond for O'Connor (h/t), E Moore for Donohoe (47), C Dunbar for Kehoe (53), S Tomkins for Nolan (63).
Ref: C Lyons (Cork).