The favourites were seldom troubled as they set up a clash with Munster runners-up Clare next weekend.
Laois had an early chance to forge ahead when a foul on Jer Quinlan led to a fourth-minute penalty, but Enda Rowland’s strike was saved by rival number one Mark Fanning.
Seven points without reply between the 16th and 24th minutes pushed Wexford into a commanding 0-13 to 0-5 lead, with Liam Og McGovern doing well at midfield while Conor McDonald was sharp in attack.
While Aaron Dunphy’s free-taking kept Laois in touch, they still trailed by 0-18 to 0-11 at half-time, with nine players on the scoresheet for Wexford.
By the time Dunphy hit the first Laois point from play after the break in the 55th minute, the visitors had extended their advantage to 0-27 to 0-15.
The only thing missing from their strong performance was a goal, with Enda Rowland keeping out a couple of Conor McDonald efforts in the 17th and 53rd minutes.
Kevin Foley marked his 100th senior appearance for Wexford when he replaced captain Lee Chin – who scored eleven points – in the final quarter.
Scorers – Wexford: L Chin 0-11 (5f, 2 65s), C McDonald 0-5, C Hearne and L Og McGovern 0-3 each, R O’Connor and C Byrne 0-2 each, S Casey 0-2 frees, S Donohoe, D Reck, T Kinsella and C Byrne Dunbar 0-1 each. Laois: A Dunphy 0-15 (11f, 2 65s), S Maher 0-2, R Mullaney, A Corby, C Comerford 0-1 each.
Wexford: M Fanning; S Reck, M O’Hanlon, S Donohoe; E Ryan, D Reck, C Foley; C Hearne, L Og McGovern; T Kinsella, R O’Connor, C McGuckin; C Byrne, L Chin, C McDonald. Subs:
C Byrne Dunbar for Kinsella (45), C Dunbar for Byrne (50), K Foley for Chin (56), S Casey for McGovern (67), D Carley for McDonald (70).
Laois: E Rolland; R Mullaney, D Conway, D Hartnett; I Shanahan, P Delaney, T Cuddy; A Corby, D Dooley; A Dunphy, G Lynch, P Purcell; J Quinlan, S Maher, T Keyes. Subs: F C Fennell for Conway (20), C Comerford for Lynch (34), M Phelan for Maher (51), R King for Quinlan (57), J Lennon for Corby (62).
Referee: S Hynes (Galway).