The O'Moore County will take on Antrim in the next round.
Laois are in the Tailteann Cup semi-finals after victory over Kildare in Tullamore yesterday.
The O'Moore County have moved to just two wins away from qualifying for next year's All Ireland Football Championship thanks to a 2-11 to 0-12 point victory.
After the game it was announced Glenn Ryan was stepping down from the Lilywhites post after a difficult season that saw Kildare relegated to Division Three of the league.
Justin McNulty says he's satisfied with the result and performance:
Laois now progress to face Antrim in the semi final this weekend.
In the other semi final, Down will face Sligo.
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