Dublin shot 21 wides but still had far too much firepower for Laois at O'Moore Park to advance to the next round of the qualifiers.
The visitors' ability to get goals was decisive as they brought Laois' season to a halt. The hosts never recovered from a disastrous start. Laois won the toss and took wind advantage but their hopes of building a lead suffered a massive double blow as Dublin struck for two goals in the opening seven minutes.
Mark Schutte got both of them, soloing in after less than half a minute to bounce a shot to the net. Conal Keaney quickly followed with a point and while Willie Hyland got the home side off the mark after five minutes, they found themselves 2-2 to 0-1 behind after seven minutes when a Shane Barrett point was followed by Schutte's second goal when he grabbed a long free from Johny McCaffrey before finishing in style.
Laois kept their composure and while they rarely looked like getting a goal in the opening half, they clawed their way back into contention. Wing-back Joe Fitzpatrick and Zane Keenan landed points and while Eamon Dillon responded for Dublin, Laois then enjoyed a great spell, with wing-forward Cha Dwyer shooting two excellent points from the out the field in rapid succession, and Keenan adding another free.
Keaney, who had a goal disallowed for a push, extended the lead with a free before Laois hit four in a row - through Joe Campion, Hyland, Keenan and a monster from Dwyer - to draw level at 2-4 to 0-10 after 24 minutes, and the home crowd were on their feet in the prospect of building an interval lead.
But Dublin again responded well. Paul Ryan pointed a free from long range before Dillon, who hit three points and three wides in the opening half, found the range.
Keenan pulled one back but Schutte continued to threaten at the other end. He pointed and after Ryan O'Dwyer also hit the target, Schutte turned provider to set up Keaney for a goal from close range to put Dublin 3-8 to 0-11 in front three minutes from the interval.
It was another huge body-blow for Laois and while Keenan and Hyland fired over points, Dillon's third effort saw Ger Cunningham's men lead by 3-9 to 0-13 at the break, with wind advantage to come.
And Dublin weren't long making good use of that wind, shooting three points rapidly after the restart from Ryan, Keaney and Dillon.
Hyland and Stephen Maher pulled back points but they badly needed a goal, and the Dublin defence was able to deal with anything thrown at them.
Ryan landed another free for Dublin to put them 3-13 to 0-15 in front, but they failed to build on that as they shot some terrible wides, giving Laois a glimmer of hope of coming with a late raid.
Matthew Whelan landed another Laois point but McCaffrey and Ryan kept the scoreboard ticking over with points for Dublin and with their full-back line of Niall Corcoran, Cian O'Callaghan and Paul Schutte in commanding form, there was no way back for Laois.
Neil Foyle, Keenan and Tom Delaney managed points for Laois but the goal they needed never came.
Instead, it was Dublin who found the net when substitute Dotsie O'Callaghan blasted home in the dying moments to crown the win and march into the next round with ten points to spare over a Laois side who just did not have the power up front to trouble the visitors.
Scorers - Dublin: M Schutte 2-1, C Keaney 1-3, P Ryan 0-5 (4f), E Dillon 0-4, D O'Callaghan 1-0, S Barrett, J McCaffrey, R O'Dwyer, D Plunkett 0-1 each. Laois: Z Keenan 0-6 (5f), W Hyland 0-4, C Dwyer 0-3, J Fitzpatrick, M Whelan, T Delaney, S Maher, J Campion, N Foyle 0-1 each.
Dublin: G Maguire; N Corcoran, C O'Callaghan, P Schutte; C Crummey, L Rushe, S Barrett; J McCaffrey, R O'Dwyer; C Boland, E Dillon, D Sutcliffe; M Schutte, C Keaney, P Ryan. Subs: S Durkin for Barrett (52), D O'Callaghan for Boland (60), D Treacy for Ryan (68), D Plunkett for Sutcliffe (70).
Laois: E Reilly; D Palmer, C Healy, B Stapleton; J Fitzpatrick, M Whelan, T Delaney; P Whelan, P Purcell; S Maher, Z Keenan, C Dwyer; T Fitzgerald, W Hyland, J Campion. Subs: J Delaney for Stapleton (35), N Foyle for Fitzgerald (43), J Walsh for Purcell (44), PJ Scully for Whelan (47), B Conroy for Maher (67).
Referee: J Ryan (Tipperary).