Wexford newcomer Colm Farrell cracked home a stunning late goal to deny Dublin the full points at Wexford Park this afternoon.
The Dubs hit three points in a row before Farrell, who was making his first league start, found the visitors' net with a measured finish.
Stephen Nolan goaled early on for Wexford from a free. The sides were level at half-time at 1-03 to 0-06 with Dublin's Stuart Mullen landing three frees.
Despite having Pedar Carton sent-off, the Dubs retook the lead and Simon Lambert missed a late chance, from 65 metres out, to win the tie.
Carton's dismissal - for his second bookable offence - forced Dublin to play out the final quarter-hour with 14 men as they sought their first league win over Wexford since 1985.
Attempting to add to their opening day victory over Antrim, Tommy Naughton's side made an encouraging start - Stuart Mullen (free) and Kevin Flynn both pointed in the opening 12 minutes, while Wexford shot six early wides.
The Model men struggled for points from play all afternoon, and indeed all bar two of their scores were from placed balls until Farrell swept home that late goal.
Wexford's first major was all about Stephen Nolan's hard work. A goal-scoring chance presented itself to the full-forward in the 14th-minute but Dublin goalkeeper Gary Maguire managed to save his shot.
Nevertheless, referee Dominic Connolly had spotted a foul on the Faythe Harriers clubman, who stepped up to slam the placed ball to the Dubs' net.
Dublin responded with points from Carton and David O'Callaghan, who had another fine game. Midfielder Lambert was unfortunate when his well-hit sideline cut bounced back off a post.
Nolan and Mullen traded frees as Dublin edged ahead before corner forward David Redmond hit two quick points - opening Wexford's account from play after all of 30 minutes.
Mullen replied with a free before his attacking colleague Flynn hit the side-netting with a late goal-scoring chance.
All that left the sides level at the break and with the tempo increasing in the second half, players like Dublin centre-back Tomas Brady and Wexford substitute Rory Jacob came to the fore.
Jacob kept his side in contention, taking over the free-taking duties from the substituted Nolan and fired over three crucial points.
Although the Dubs, with former footballer O'Callaghan picking off two superb points, hit the front again in the closing stages, Farrell was able to save Wexford's bacon as he got in on the end of a long free to bulge Maguire's net.
Wexford: D Fitzhenry; M Travers, K Rossiter, P Roche; R Kehoe, D Morton, C Kenny; C Farrell (1-00), J O'Connor; W Doran, M Doyle, M Jacob; D Redmond (0-02), S Nolan (1-04, 1-04f), R Jacob (0-03, 0-03f).
Subs: T Dwyer for O'Connor (29 mins), D Lyng for Doran (half-time), D Stamp for Nolan, E Martin for R Jacob (both 62), S Doyle for Redmond (69).
Dublin: G Maguire; P Brennan, S Hiney, P Bergin; M Carton, T Brady, J Boland; J McCaffrey (0-02), S Lambert (0-01); S Mullen (0-07, 0-06f), D O'Dwyer, R O'Carroll; D O'Callaghan (0-03), K Flynn (0-01), P Carton (0-01).
Subs: P O'Driscoll for Flynn (43 mins), P Kelly for O'Carroll (58), A McCrabbe for O'Dwyer (65).
Referee: Dominic Connolly (Kilkenny).
