Wexford had the ideal start with a Rhys Clarke fourth-minute goal, after Gary Maguire had saved his initial effort. Wexford continued to edge things and led 1-11 to 0-10 at the interval.
Conal Keaney struck over two superb long-range points while a Paul Ryan shot from a 21m free crept over the line.
That was enough to give the visitors a two point lead, but Gary Moore and Paul Morris had the sides back level.
Two pointed Paul Ryan frees gave the Dubs the edge going into the closing minutes and although Wexford pressed strongly they could only manage a late Rhys Clarke pointed free.
DUBLIN: G Maguire; C O’Callaghan, P Kelly, J Doughan; J Boland, C McCormack, M McCaffrey; S Durkin, M Quilty; R Mahon (0-1), R O’Dwyer (0-2), C Keaney (0-2); M Schutte (0-1), P Ryan (1-7f), E Dillon (0-2).
Subs: C Crummy for McCaffrey (h-t); C Cronin for Mahon (54); P Winters for Schutte (65).
WEXFORD: M Fanning; J Tonks, K Rossiter, C Kenny; A Shore (0-1), L Chin, R Kehoe; B Jordan, D O’Keeffe (0-2); S Tomkins (0-1), P Morris (0-2), I Byrne (0-6, 5f); G Moore (0-1), R Clarke (1-1, 0-1f), K Foley.
Subs: H Kehoe for Jordan (h-t); C O’Shaughnessy for Tonks (53); R Jacob for Foley (57); C Devitt for Byrne (61).
Referee: J Keenan (Wicklow).