A second-half push from Kieran McGeeney's side did little to worry the reigning Ulster champions, with both sides putting ten points on the board before the final whistle.
A masterclass from Tony Kelly left Wexford wanting, with Davy Fitzgerald's side unable to dampen the Ballyea man's influence.
A ten-point lead for the Banner at the break put them firmly in charge for the second half, with a 56th minute goal from Kelly killing any hopes of a Wexford revival and cementing their exit from this year's Championship.
Cork also have a long winter ahead as Tipperary saw them out, winning 2-18 to 1-17.
Poor conditions in the Gaelic Grounds made for a slow start for the Rebels, but a goal from Patrick Horgan just after the first water break brought them back into contention with just two points separating the sides at half time.
The second half was an equally close affair, with nothing between the teams with 64 minutes gone.
A 68th minute goal from Tipperary's Jake Morris was the fatal blow in the end, keeping their chances of retaining the All-Ireland title firmly intact.
The final match of the day proved worth the wait as Kilkenny mounted a heroic comeback to overcome Galway.
The Cats held onto their provincial title, winning 2-20 to 0-24 to bag their 73rd Leinster championship.
But far from Galway to make it easy for Brian Coady's side, the Tribesmen dominated the first half and lead by five points with 55 minutes gone until Richie Hogan and TJ Reid conspired to turn the game on its head.
Two goals in the space of two minutes gave Kilkenny the smallest of lead's with 15 minutes to play, but Galway kept a tight grip on their lead, looking like they had enough to get over the line.
Three points from Hogan, Conor Browne and Martin Keoghan in the final few minutes saw no reply from Galway and no Leinster title for the Connacht men.
