Two goals by Kieran Kelly earned Laois a place in the semi-final at the expense of Kildare in this replay on Saturday.
Kelly's first goal arrived on the quarter-hour and Laois went on to lead 1-6 to 0-6 at half-time.
Kildare continued to press hard for the duration of the second half, but they couldn't close the gap and Kelly's second goal put the result beyond doubt.
Laois: M Leigh; J Keogh, B Gaynor, P McDonald; T Kelly, J Higgins, A Fennelly; P Clancy, D Rooney; K Kelly (2-0), B Fitzpatrick (0-1), M Hovendon; S Kelly (0-3), G Kavanagh (0-5), M Dunne (0-2). Subs: M Lambe for Hovendon, J Behan for Rooney, D Mullins for Lambe.
Kildare: P Canavan; J O'Malley, P Mullarkey, M Wright; D O'Hanlon, D Byrne, S White; R Sweeney, A McHugh; C Reilly (0-4), N Naughton (0-1), D Winders; A McAndrew (0- 1), T Rossiter (0-3), K Donnelly (0-3). Sub: E Flanagan for Winders.
Referee: P Fox (Westmeath).