In an entertaining game at Ferrycarrig Park between the two promoted sides, Curran fired Harps ahead from the spot after 23 minutes.
Wexford, needing a result to avoid the gap between them and Harps extending beyond five points, got back level through Andy Mulligan’s well-taken equaliser six minutes after the restart.
In the First Division, Cobh Ramblers lost 1-0 at Drogheda United despite creating enough chances on the night to have taken at least a draw.
Early on, Markus Gustavsson forged a great opportunity for Cobh only to see his header saved by Stephen McGuinness. Aaron Ashe was more clinical with his effort midway through the half. He was given the time and space from a pass by Marc Griffin to beat Paul Hunt.
Although the Rams carved open the hosts on a number of occasions, Drogs might have extended their winning margin had Colm Deasy or Sean Thortnton been more clinical when bearing down on goal.
More floodlight problems at Tolka Park forced Shelbourne to host their meeting with Athlone Town early and, despite only 447 fans showing up, it didn’t impact on the pitch as the Reds won 2-1.
Their fifth win of the season was secured through goals from Aidan Collins and James English, either side of Daniel Purdy’s equaliser for Town. All the goals came in the first half, with Athlone nearly grabbing a point late on when Alan O’Sullivan’s header was saved by Jack Brady.