Galway 2-22 Wexford 1-14
Ger Farragher top-scored with 0-13 as Galway beat Wexford at Nowlan Park to make the Leinster Championship's last-four.
The Tribesmen held a 1-9 to 0-6 interval lead thanks to Joe Canning's injury-time goal, with Diarmuid Lyng keeping Wexford in touch.
Tomas Watters' 55th-minute goal brought Wexford to life.
But despite the efforts of Lyng (0-11), a Kevin Hynes goal steadied Galway.
Wexford's woes were summed up in the closing stages when David Redmond and Lyng were both sent-off.
This was a game which could have been characterised by missed opportunites and dismissals - Galway also had half-forward Andy Smyth dismissed in the 54th minute - but ultimately some excellent scoring shone through on a dull evening in Kilkenny.
Farragher and Lyng were coolness personified for most of this encounter between the recently crowned National League champions, with both players showing some enviable accuracy in front of the target.
Castlegar clubman Farragher was in terrific form as he struck six early points to nudge Galway into a 0-7 to 0-3 lead by the 26th minute.
Lyng (0-2) and Harry Kehoe had Wexford's opening scores, and with Keith Rossiter doing an excellent man-marking job on Joe Canning, the Portumna ace was confined to just one point in first half.
However, the ever dangerous Canning made the breakthrough in first-half injury-time. With Rossiter committing a foul on the 21-year-old, he stepped up to smack the resulting 21-metre free to the back of the Wexford net and give his side six-point interval lead.
Even still, Galway manager John McIntyre will have been disappointed with his side's wides tally of 11 over the opening 35 minutes.
The Division 1 champions' strike-rate improved in the second half, but they did miss some gilt-edged opportunites in a 10-minute spell after the restart.
Galway added four wides to their tally as Wexford were able to close the deficit with Lyng continuing to slot placed balls through the uprights.
Just a goal separated the sides at 1-12 to 0-12, 13 minutes into the second half; but the Tribesmen then seized the inititive with three unanswered points.
Farragher, Damien Hayes and Joe Canning added points to ensure restore the six-point buffer as the game entered the final quarter.
Galway were now reaping rewards in attack, with Joe Canning now operating at right half-forward and Hayes switched to full-forward.
Smyth received a straight red card for a elbow-led challenge on Wexford midfielder Colm Farrell, and while that was a major dent with Wexford quickly snatching a goal, Galway remained on top.
Wexford substitute Waters slipped home a goal, after a Lyng free dropped short, to cut the deficit to three points - but this was as close as Wexford would get in the closing stages.
McIntyre's men simply turned on the turbo switch in the closing 15 minutes, with Farragher to the fore in terms of scoring. He collected his tenth point in the 57th minute, before substitute Kevin Hynes scored his first Championship goal.
Hynes was only on the pitch for two minutes when he took a great pass from Damien Hayes and got the better of Wexford goalkeeper Noel Carton from close range.
Lyng kept his side battling away with some well-taken scores, but Galway were now firing over from all angles as Aidan Harte, David Burke, Farragher and Aonghus Callanan all tagged on points.
There was no way back for Wexford who missed out on a goal when full-forward Stephen Banville failed to ripple the net following an excellent catch. The Model men's frustrations were obvious as substitute Redmond received his second yellow card fo a foul on the excellent Hayes, and Lyng also walked late on for a poorly-timed challenge on David Burke.
GALWAY: C Callanan; D Joyce, S Kavanagh, O Canning; D Barry, T Óg Regan, D Collins; G Farragher (0-13, 0-10f, 0-1 '65'), D Burke (0-1); D Hayes (0-2), C Donnellan, A Smyth (0-1); A Harte (0-1), J Canning (1-3), J Gantley.
Subs used: I Tannian for Donnellan (46 mins), K Hynes (1-0) for Gantley (58), A Callanan (0-1) for Harte (66), J Lee for Regan (68), A Cullinane for Collins (70).
WEXFORD: N Carton; L Prendergast, K Rossiter, C Kenny; R Kehoe, D Stamp, M Travers; H Kehoe (0-1), C Farrell; M Jacob, E Quigley (0-1), D Lyng (0-11, 0-8f, 0-1 '65'); R Jacob (0-1), S Banville, P Atkinson.
Subs used: D Redmond for Travers (13 mins), T Waters (1-0) for R Kehoe (43), P Morris for M Jacob (66).
Referee: John Sexton (Cork)