Ruairi O'Connor tormented the Wicklow full-back line, scoring 1-6 as Laois pulled away in the second half at Greystones.
The dismissal of Ambrose Doran for an off-the-ball incident in the 52nd minute didn't deter the Lake Men, who outscored their hosts by seven points in the last 20 minutes.
Wicklow had led 1-5 to 0-7 at half-time as Seanie Furlong marked his return to county action with a well taken goal after Laois were guilty of playing around in defence.
Stern defending kept the Laois attack at bay in the first half, but 2-1 within the opening five minutes of the second half gave the visitors a commanding lead - Gary Walsh got the other goal.
Wicklow had chances to come back into it but too many wides at crucial stages didn't help their cause.
Laois continued to kick points at will, with some brilliant efforts from O'Connor and substitute Sean Ramsbottom especially.
Scorers - Laois: R O'Connor 1-6 (0-3fs), G Walsh 1-4 (2 '45s'), A Doran 0-3, S Ramsbottom 0-2, J Farrell, R Munnelly 0-1 each. Wicklow: S Furlong 1-3 (0-3fs), M Jackson (1f), P Byrne, A McLaughlin, D Boothman, B Kennedy 0-1 each
Laois - E Keogh; C Lennon, K Lillis, G Dillon; D Strong, A Farrell, C Begley; K Meaney, D Kingston; J Farrell, A Doran, M Campion; R O'Connor, G Walsh, P Kingston. Subs: C Murphy for M Campion (10), R Munnelly for J Farrell (ht), S Attride for G Dillon (ht), S Ramsbottom for D Kingston (46), J Farrell for K Meaney 66).
Wicklow - M Jackson; C Hyland, R O'Brien, B Kennedy; D Hayden, J Snell, J Crowe; D Boothman, A McLoughlin; R Finn, S Kelly, M Kenny; P Byrne, S Furlong, J McGrath. Subs: E Murtagh for S Kelly (47); M Cullen for J Crowe (57); C Ffrench for M Kenny (58); M Fitzsimons for A McLaughlin (65).
Ref - J King (Dublin)