Jack Guiney hit an injury-time free for Wexford to force a replay after Eamonn Dillon's late goal looked like giving Dublin an unlikely victory at Wexford Park.
The sides ended level at 1-17 to 1-17, but after shooting 14 wides Dublin will especially be relieved to get another chance.
Five minutes from time Wexford looked certain to push on to victory when captain Garrett Sinnott hit his fourth point from play to open up a three-point lead for the home side.
But substitute Dillon fired Dublin ahead three minutes from time with a crisp ground stroke, only for Guiney to hit his sixth free of the night, to add to his first-half goal, as the sides must try again to find a winner.
The fact that Wexford trailed by only a point at the break was somewhat of a miracle considering the ponderous start they lodged in the first ten minutes.
Rory Jacob had fired the opening score of the game after 15 seconds for Liam Dunne's side, but they went on to concede six scores on the bounce to trail by 0-6 to 0-1 by the 11th minute.
But despite their poor start Wexford began to grow into the game and with Jack Guiney in great form from dead balls and Jacob taking every chance that came his way, Liam Dunne's side closed to within two points by the 18th minute.
With Paul Ryan on the bench, Joey Boland was proving a more than adequate free-taker and he extended Dublin's advantage with two quick frees by the 26th minute.
But after Garrett Sinnott and Padge Doran replied, Guiney hit a super goal for the Yellowbellies on the half-hour mark after Eoin Quigley carried well into the danger zone.
But critically Dublin finished the half well as a Boland free was followed by a battling score from Danny Sutcliffe to give Anthony Daly's side a 0-12 to 1-8 lead at the break.
Neither side managed to gain the upper hand in the third quarter, but after the introduction of Lee Chin before the break, Wexford began to gain the upper hand around midfield.
Guiney landed a free for Wexford in the 49th minute and his forward colleagues followed it with three points from play to give the home side a two point lead.
And from there the game turned as Dublin suddenly found their scoring touch.
Mick Carton hit a huge point from distance before Dillon hit the net with a ground stroke three minutes from time.
But Guiney took the late chance to force the replay and the extra game will suit both sides ahead of a potential semi-final with the All-Ireland champions Kilkenny.
Wexford: M Fanning; E Moore, T Waters, K Rossiter; R Kehoe, A Shire, C Kenny; H Kehoe (0-01), C O'Shaughnessy; D Redmond, E Quigley, G Sinnott (0-04); J Guiney (1-08, 0-06f), P Doran (0-01), R Jacob (0-03).
Subs: L Chin for O'Shaughnessy (28 mins), P Moris for Quigley(53 mins), PJ Nolan for H Kehoe (59 mins).
Dublin: G Maguire; N Corcoran, P Kelly, P Schute; M Carton (0-02), L Rushe, S Durkin (0-01); J McCaffrey, J Boland (0-09, 0-08f); C McCormack (0-01), R O'Dwyer, D Sutcliffe (0-03); D O'Callaghan, C Keaney, D Treacy.
Subs: N McMorrow for O'Dwyer (6-12 & 48-51 mins blood), E Dillon (1-00) for Treacy (44 mins), P Ryan (0-01) for O'Callaghan (46 mins), S Lambert for Durkin (55 mins), R Trainor for P Schutte (58 mins), M Schutte for McCormack (63 mins).
Referee: Diarmuid Kirwan.