Clare have knocked Wexford out of the championship for the second season in a row.
Davy Fitzgerald's side were behind by 11 points twice, but eight unanswered points cut the gap to two, 1-15 to 1-13, in the 40th minute.
A much-needed Tony Kelly free in the 42nd minute was Clare's first score since the 31st minute.
Brian Lohan's side kicked back into gear after that and points followed from Aidan McCarthy, Kelly, and David Reidy to give the Banner a six-point lead.
Wexford kept fighting until the very end and points from Lee Chin and Rory O'Connor cut the gap to three on 66 minutes.
However, a goal from Clare substitute Gary Cooney killed off the Wexford challenge in the 72nd minute.
Chin scored at the other end but it wasn't enough for Fitzgerald's side.
The final score was 2-25 to 2-22 in favour of Clare.
Elsewhere Waterford beat Laois 3-23 to 2-21 at Nowlan Park to seal their spot in the round two draw that will take place on Monday.
Kevin Moran, Patrick Currand and Stephen Bennett all found the back of the net for the Déise.
Brian Cody has the chance to win his 17th Leinster Senior Hurling title as Kilkenny manager this evening.
The Cats face Dublin in the provincial decider, where 18,000 will be watching on at Croke Park at 7.30pm.
