Ashbourne held on to claim an 18-10 win despite a late fightback from Gorey RFC.
The Wexford club scored a try with five minutes remaining to make it 15-10, but a late penalty secured the win for Ashbourne.
It took extra-time to separate Enniscorthy RFC and Wicklow, in a game which also produced the odd sight of the home side wearing Leinster Rugby blue to avoid a colour clash with the visitors.
Scorthy led 16-9 thanks to two drop goals as the game entered injury time, however, Wicklow scored a late converted try to level matters.
They carried that momentum into extra-time and took a 16-22 lead with a penalty and a drop goal.
Despite Enniscorthy’s relentless pressure in attack in the closing stages, the Wicklow defence stood strong and they held on to claim their place in the semi-final of the Cup.
Bank of Ireland Provincial Towns Cup Quarter-final results
Ashbourne RFC 18 Gorey RFC 10
Enniscorthy RFC 16 Wicklow RFC 22 (AET)
Skerries RFC 2nd XV 21 Clondalkin 16
Tullow RFC 50 North Kildare RFC 0
Bank of Ireland Provincial Towns Cup Semi-final draw
Both fixtures will take place on Sunday, 2nd April, and will kick-off at 3pm.
Ashbourne RFC v Tullow RFC (Venue: Edenderry RFC)
Wicklow RFC v Skerries RFC 2nd XV (Venue: Cill Dara RFC)