Despite playing with 14 men for the last seven minutes after sub Willie Dunphy got a straight red for a strike off the ball, Laois scored three points without reply in that time, including two from Maher, to wrap up the win.
Laois racked up 1-10 in the first half as their speed and strength was too much for their hosts, who were only in the contest thanks to a goal against the run of play from Paul Divilly in the 16th minute. Laois scored five points on the trot at that stage and they finished the first half strongly with a well-taken Brian Dunne goal for a six-point half-time lead. Kildare fought back, however, narrowing the gap to four on two occasions but Laois were always in control and scored five unanswered points to claim victory.
LAOIS: E Reilly; J A Delaney, D Maher, B Campion; J Fitzpatrick, M Whelan 0-2 (65s), C Healy 0-1; J Walsh 0-1, S Dollard; B Dunne 1-0, Z Keenan 0-1, W Hyland 0-4; J Brophy, T Fitzgerald 0-1, S Maher 0-9 (7fs).
Subs: W Dunphy for Dollard, 46; B Conroy for Keenan, 67.
KILDARE: P McKenna; P Keegan, F Ó Muineacháin, P Curtin; K Divilly, R Hoban 0-2 (1f, 1 65), P Reidy; D Butler, N Ó Muineacháin; M Moloney 0-1, P Divilly 1-5 (4fs, 1 65), R Kelly; T Murphy, D Kennedy, G Keegan 0-2.
Subs: P Downey for Kennedy (h-t); E O’Neill for N Ó Muineacháin (h-t); B Deay for Murphy (36); C O’Hehir for P Divilly (58).
Referee: T Carroll (Offaly).