Offaly and Laois claimed first-round Leinster Under-21 Football Championship wins, while Longford and Westmeath drew.
Offaly travelled to Taghmon in Wexford and Adam Shelly’s goal helped the Faithful to a 1-16 to 0-06 win.
They will play Kildare in Athy on 5 March in the quarter-finals.
In Baltinglass, Evan Costello scored two late points to hand Laois a 0-10 to 0-09 victory over Wicklow.
The O’Moore County will meet the winners of the Longford-Westmeath replay after the sides played out a draw in Newtowncashel, 1-12 to 0-15 after extra time.
The replay has been set for Mullingar on Wednesday at 7.30pm.