Offaly will face Laois or Louth in the Leinster U-21 Football Championship semi-final after seeing off the challenge of Wexford in Gracefield.
In very difficult conditions, the sides were locked at 0-2 apiece at half-time but a goal from Edenderry's Jordan Hayes early in the second-half gave Offaly the advantage.
Captain Ruairi McNamee was to the forefront as Offaly built a 1-6 to 0-2 lead and while Wexford put in a late rally, Offaly held on for the win.
After a slow start, Louth proved too strong for Wicklow and came through by 1-13 to 0-9.
Elsewhere Longford overcame Kildare by 2-16 to 0-10 while Dublin had a comfortable 2-14 to 0-6 win over Westmeath.