With the sides tied 0-15 to 1-12 after 60 minutes, after Wexford’s Rory O’Connor had landed a late equaliser, the hosts proved far stronger in the closing stages as they confirmed their semi-final spot by a four-point margin.
There was little to separate the sides in a cagey first half, with two points by Dublin midfielder Ciaran Dowling ensuring a 0-6 to 0-6 stalemate.
The visitors looked to have landed the decisive blow when substitute Ronan Hayes netted midway through the second half but the hosts bounced back, before falling behind in the 60th minute to a Colin Currie free.
There was sufficient time for O’Connor to reply and the same player added the first two scores of extra-time to push Wexford clear. Dublin responded through points from Cillian Byrne and Johnny McGuirk but their challenge petered out as Wexford drove on through by O’Connor, Conor Hearne, and Eoin Kelly.
Wexford are joined in the semi-finals by holders Kilkenny, who recorded a comfortable 3-25 to 1-13 victory over Offaly in Nowlan Park.
There were 13 points between the sides at the break with James Bergin’s goal helping the hosts to a 1-14 to 0-4 lead, with Bergin hitting 2-3.
At Cusack Park, Westmeath did just enough to progress as they overcame neighbours Meath on a 1-17 to 0-15 score.
The hosts led 0-10 to 0-5 at the break and a Marcus Kennedy goal drove them on.
In O’Moore Park, Laois bounced back from the disappointment of losing to Offaly in their opening outing as they enjoyed a 3-20 to 0-9 victory over Carlow, with Aaron Dunphy hitting 1-7.