A remarkable period immediately after half-time turned this tie on its head and sent Kildare through to a Leinster semi-final against Dublin.
Laois led by a point at half-time but were rocked by the concession of two goals and three points in three minutes and 15 seconds at the start of the second half.
Cathal McNally kicked a point from the restart. Graham Brody's short kick-out was intercepted by Alan Smith and he fed Eamonn Callaghan, who slid his shot expertly below the Laois goalkeeper. Callaghan followed up with a point before Smith's shot for the posts was palmed to the net by McNally.
Kildare added a couple more points and though Donie Kingston offered brief hope with a 47th minute goal, Eoghan O'Flaherty's resounding finish at the other end five minutes later removed any doubt. It was one-way traffic from there to the end.
Niall Donoher opened the scoring in the second minute and that started a flurry of scores in the next four minutes, with each side responding to the other.
It was nip and tuck for the rest of the half but Laois were getting a spectacular return from their half-forward line.
Niall Donoher and Evan O'Carroll shared six points from play in the first half, with O'Carroll in particular outstanding, adding ball-winning to his scoring threat. He also slotted a free from outside the 45m line just before half time to give Laois a 0-9 to 0-8 interval lead.
Unlike the drawn game, Kingston spent the majority of his time at the edge of the square and won most of what came his way. Mark Donnellan came to his side's rescue, diving to his right to save Ross Munnelly's kick. O'Flaherty levelled after a delightful diagonal kick-pass from Padraig O'Neill but Donoher pushed Laois ahead once more with a lovely outside-of-the-left-boot kick.
Laois had failed to create one clear goal opportunity the previous week but they wasted their second in a short space of time when Brendan Quigley careered forward but blazed wide from a promising position.
Kildare spurned three in the first game, with Alan Smith hitting the crossbar.
Kildare dropped deeper as the half wore on and hit Laois with speed on the counter. The worked the ball forward fabulously for O'Neill to put Smith in but Brody advanced smartly to deny the former All-Star nominee's left-foot shot with a brilliant dive to his right.
Kildare did hit the front for the first time with points from Murnaghan, and an O'Flaherty free that was brought forward by Anthony Nolan for dissent.
Laois had a period of superiority at midfield, with John O'Loughlin making a couple of fine catches and they kicked four of the next five points from Kingston (free), Tom Shiel, O'Carroll and Donoher. White launched a wonderful score from 40m and O'Flaherty curled his third before O'Carroll's free gave Tomás Ó Flatharta's crew the edge at half-time but it was an edge that they lost very quickly.
Scorers - Kildare: E O'Flaherty 1-4(0-2fs), P Fogarty 0-4, K Murnaghan 0-1, G White 0-1, P Cribbin 0-2, E Callaghan 1-1, C McNally 1-2, O Lyons 0-1, P O'Neill 0-1, N Kelly 0-1. Laois: D Kingston 1-2(0-2fs), E O'Carroll 0-5(1f, 1 45), N Donoher 0-3, T Shiel 0-1
Kildare: M Donnellan, C Fitzpatrick, M O'Grady, O Lyons, K Murnaghan, F Conway, E Bolton, P Cribbin, G White, P O'Neill, E O'Flaherty, C McNally, E Callaghan, P Fogarty, A Smith. Subs: E Doyle for Conway blood (21-29), Doyle for Conway (ht), T Moolick for McNally (52), D Hyland for Bolton (57), N Kelly for Smith (59), H Lynch for White (64), M Conway for Callaghan (67)
Laois: G Brody, S Attride, M Timmons, R Kehoe, D Strong, C Begley, D O'Connor, B Quigley, J O'Loughlin, N Donoher, C Boyle, E O'Carroll, R Munnelly, D Kingston, T Shiel. Subs: E Culliton for Brody blood (8-14), P Kingston for Munnelly (43), J Finn for Shiel (51), G Hanrahan for O'Connor (60), G Dillon for Strong (65), B Sheehan for Donoher (65), E Lowry for Boyle (65)
Referee: A Nolan (Wicklow)
Sunday Indo Sport