Stephen Duff's side managed to win the second half after a poor first half showing.
Laois are facing into a relegation final after they were convincingly beaten by Tipperary in Callan on Saturday.
The O'Moore County's fate was effectively sealed when they reached the break without a score on the board, trailing by 14 points.
The final score in Callan was 1-15 to 1-4.
Stephen Duff's side now must face Kildare in the Senior Championship Relegation Final after the Lilywhites were narrowly beaten by Donegal.
Duff says despite the disappointing first half performance, his players can be proud of how they applied themselves:
The relegation final takes place on Saturday at Netwatch Cullen Park, Carlow at 1.30pm.
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