Dublin came good when it mattered most as second half goals from Diarmuid Connolly and Michael Daragh Macauley paved the way for an 11-point win for the reigning All-Ireland and Leinster champions at Croke Park.
For large stages of the opening half it looked like Laois would claim a first Championship win over Dublin since 2003, but Jim Gavin's side upped their game in the second half to book a semi-final berth.
Laois showed from early on that they meant business in this game, and shot the opening wide after just 17 seconds through Billy Sheehan.
Dublin quickly got on the scoresheet at the opposite end following a good move involving Darren Daly, Paddy Andrews and Alan Brogan, with the latter opening the scoring.
But Laois took the lead after three minutes thanks to two quick-fire Ross Munnelly points and the Midlanders wouldn't trail for the remainder of the half.
Defender Darren Strong added Laois third point in a row inside 90 seconds and although Dublin were creating scoring chances they weren't capitalising.
Goal chances went amiss in the fifth, 11th, 15th and 17th minutes, through a combination of excellent goalkeeping and the posts and the crossbar also being tested.
Graham Brody was immense for Laois during the opening half, and pulled off his first save of the day in the fifth minute, blocking out a Paddy Andrews goal shot, with Cluxton slotting over the resulting 45.
That cut the gap to the minimum, but Laois continued to remain in front despite some bad wides.
After 10 minutes the wides count stood at 4-2 in Laois's favour, but crucially the O'Moore's were creating far more scoring chances.
At this stage Dublin had only take two of their scoring chances, and this didn't get much better over the next 10 minutes.
By the 20th minute Dublin had added scores from Paul Flynn, Bernard Brogan and Cian O'Sullivan, but Laois led 0-7 to 0-5, after they added scores from Munnelly, Strong and James Finn.
Dublin worked hard and levelled the tie after 32 minutes following an Eoghan O'Gara score, with five of Dublin's starting forwards now on target.
But Laois finished the half strongly and held a two-point lead at half-time, after Donal Kingston pointed their first score to come from a free to ensure a 0-10 to 0-8 interval score-line.
The first half performance certainly gave Laois players, management and supporters great heart, but the second half was to provide a different story.
Dublin burst out of the blocks, with substitute Kevin McManamon leading the charge with two early points, while scores from Paul Flynn and Cluxton ensured a 0-12 to 0-10 lead after 43 minutes.
Dublin never looked back from this, and although Laois responded on occasion with scores, like one from substitute Niall Donoher in the 45th minute, the Metropolitans were beginning to take a firm grip on matters.
James McCarthy quickly cancelled out Donoher's point, before Dublin's first goal arrived in the 47th minute.
A relatively quiet Diarmuid Connolly certainly made his mark, as he rifled the ball to the right of Brody at the Hill 16 end to send the Dublin supporters into raptures and ensure a 1-13 to 0-11 lead.
Munnelly kept the scoreboard ticking for Laois, but Macauley fired Dublin's second goal at the start of the final quarter and from there on their was no way back.
Laois did match Dublin point for point on three occasions over a nine-minute spell, but Gavin's magic came to the fore yet again late on.
Dublin's bench certainly proved its worth in the closing stages with second half subs Dean Rock and Cormac Costello getting in on the scoring act.
The duo helped contribute equally to Dublin's six unanswered points in the closing five minutes with Rock first firing three points in a row from frees, and then Costello slotting over three quick points from play in a two-minute spell at the death, to ensure an 11-point win.
DUBLIN: S Cluxton(0-2, 2 45); P McMahon, R O'Carroll, J Cooper; J McCarthy (0-1), N Devereux, D Daly; MD Macauley (1-0), C O'Sullivan (0-1); P Flynn (0-3), P Andrews (0-1), D Connolly (1-1); A Brogan (0-1), E O'Gara (0-1), B Brogan (0-1, 1f). Subs: K McManamon (0-2) for B Brogan (24); J McCaffrey for Daly (29); B Cullen (0-1) for O'Gara (44); C Costello (0-3) for A Brogan (50); D Rock (0-3, 3f) for O'Sullivan (59); P Mannion for Andrews (67).
LAOIS: G Brody; P McMahon, P Begley, P O'Leary; D Strong (0-2), S Attride, C Begley; K Meaney, J O'Loughlin (0-1); J Finn (0-1), D Kingston (0-3, 2f), B Sheehan; R Munnelly (0-7, 2f), C Meredith, D Conway (0-1). Subs: N Donoher (0-1) for Sheehan (31); E O'Carroll for D Kingston (Blood 37-41); E O'Carroll for D Kingston (Blook 43-45); E Lowry for Meaney (50); R Kehoe for Attride (59); E O'Carroll for Conway (64); P Kingston for Finn (67).
REFEREE: Padraig Hughes (Armagh)