The Ballybofey outfit traveled to Ferrycarraig hoping for three vital away points but had to settle for a share of the spoils.
Former Derry City striker Ryan Curran put Harps ahead in the 24th minute form the penalty spot.
But Wexford’s equaliser was scored by Andy Mulligan six minutes into the second half.
Harps pushed for the winner but it just didn’t come.
Ollie Horgan will be happy enough with his side’s start to the campaign with 11 points on the board and sitting mid-table.
It’s very much a “building season” for Harps but they must continue to hope to win at home and snatch as many points away if they are to consolidate their place throughout the season.