Jimmy Barry-Murphy's Cork recovered from a six-point half time deficit to defeat a gutsy Wexford side by 0-18 to 0-14 in gusty conditions in Pairc Ui Rinn.
Wexford and Cork traded two early scores each before the visitors hit six points on the trot with the wind in their favour. Ian Byrne adding a number of scores from play.
Cork were reliant on Pat Horgan set-piece accuracy in the opening 35 minutes but trailed by 0-13 to 0-7.
Conor Lehane began causing serious problems after the break but Wexford led by0-14 to 0-9 after 41 minutes.
They would fail to score again as the Rebels hit nine unanswered points to secure a semi-final with Dublin.
Seamus Harnedy and Paudie O'Sullivan hitting late scores.