Tommy Bonner's og gave Wexford the two goal cushion with 34 minutes left in the game.
Harps however kicked into gear and pulled one back immediately through Kevin Mc Hugh but Bonner's night was to get even worse as he was sent off in the 69th minute.
The point was secured for Harps three minutes into injury time with Packie Mailey hitting the back of the net.
The Ballybofey outfit sit 6th in the table 10 points of the leaders Shelbourne.
Harps boss Ollie Horgan said afterwards that it was a point gained.