Laois also learned the identity of their opponents next weekend.
Offaly recorded their first Leinster Senior Football Championship win since 2016 yesterday.
Despite a late comeback from Carlow, it finished 3-14 to 20 points in Bord na Móna O'Connor Park.
Niall McNamee, Jordan Hayes and Bernard Allen the goal scorers, with Allen top scoring with a tally of 1-4.
They advance to the face Kildare next Sunday at 5:30 in MW Hire O'Moore park in Portlaoise in a Leinster Quarter-final.
Another of the quarter-final ties will see Mike Quirke take his Laois footballers to face Longford next Sunday.
That's after Longford overcame Louth by 2 points yesterday.
Throw in for that one will be 1:30.