Goals from a Mark Barry from a penalty and another from Evan O’Carroll either side of half-time laid the platform for the five-point win.
Kildare shot into an early two-point lead courtesy of Darragh Kirwan and a Shane Farrell free but they were wasteful kicking five wides in that opening quarter.
Laois punished them with Evan O’Carroll and Niall Dunne points before Darragh Kirwan edged Kildare ahead again.
Laois had momentum and when Shea Ryan conceded a penalty – Mark Barry slotted home. Ryan got a black card for his troubles.
Kildare played their best football when down to fourteen. Kevin Feely, Kirwan and Shane Farrell (with two) had the Lilywhites two up as half-time approached. Mark Barry and Conor Heffernan had time to level it at 0-7 to 1-4.
Laois returned with the bit between their teeth and four in a row pushed them into a deserved four-point lead.
It took Kildare fourteen minutes to reply but it was only a false dawn as a more determined and direct Laois outfit struck for goal number two. Evan O’Carroll moved them five ahead and into a semi final spot.
Scorers – Kildare: S Farrell 0-6 (3 frees,1’45), D Kirwan 0-3, K Feely, N Kelly, A Beirne 0-1each. Laois: M Barry 1-2 (1 penalty,1 free), E O’Carroll 1-1, K Roche 0-4 (3 frees,1 ’45),P Kingston, E Lowry, N Dunne, C Heffernan 0-1 each.
Kildare: M Donnellan, R Burke, S Ryan,M O Grady, T Archbold, B Byrne, J Sargent,A Masterson, K Flynn,S Farrell,D Kirwan, P McDermott, P Woodgate N Kelly, K Feely. Subs: R Houlihan for R Burke 42, A Beirne for A Masterson 44, L Killian for T Archbold 53, E Doyle for S Ryan 56, D Swords for S Farrell 68.
Laois: K Roche, B Dempsey, J Kelly, M Timmons,S Lacey, B Byrne, S Fingleton, D Larkin, C Heffernan, M Barry, E O’Carroll, K Swayne, E Lowry, N Dunne, P Kingston. Subs: R Murphy for K Swayne 56, M Dempsey for E Lowry 65, K Lillis for C Heffernan 68, E Bughie for N Dunne 69, B Daly for E O Carroll 70.
Referee: T Murphy (Galway)