Wexford won a repeat of last year's Leinster final against Kilkenny to book their place in next weekend's Walsh Cup final.
The Yellowbellies took a six-point lead into half-time thanks to a Michael Dwyer goal.
The Cats threatened a second-half comeback when goalkeeper Eoin Murphy blasted a penalty to the net, but it was snuffed out by Davy Fitzgerald's men.
Aidan Nolan scored their second three-pointer, and they drove on from there to win on a scoreline of 2-18 to 1-9 in Callan.
Galway await in the final after they overcame Dublin at Parnell Park by 0-19 to 0-18.
It was a good start to life under Shane O'Neill, as the Tribesmen returned to the scene of their exit from last year's Championship and claimed the victory.
They hit the last three points of the first half to take a one-point lead into the break. The second half was nip and tuck, as Mattie Kenny's Dubs closed the gap to the minimum on no fewer than seven occasions.
But they never managed to draw level, as Galway held on to progress to Sunday's final.
Meanwhile, Offaly won the Kehoe Cup, beating Antrim in a high-scoring contest by 1-16 to 1-15. Oisin Kelly scored the winning point in second-half added time in Navan.
Ben Conneely, Offaly captain, after receiving the Kehoe Cup with Jim Bolger and Pat Teehan representing Leinster Council. pic.twitter.com/UxG0MoM6uv— Official Offaly GAA (@Offaly_GAA) January 12, 2020