Colm O'Neill cracked home two first-half goals as Cork recorded their second Division 1 win in Portlaoise.
O'Neill's strike helped the Rebels break into a comfortable 2-11 to 0-05 interval lead.
The visitors were reduced to 14 men just after the restart, following a second yellow card for Pearse O'Neill.
MJ Tierney landed three points as Laois outscored the Munster men by 0-05 to 0-03 in the closing 35 minutes, but Cork had done enough to claim the result.
Laois started with plenty of purpose and snatched a 0-02 to 0-00 lead with Ross Munnelly opening the scoring after 15 seconds.
John O'Loughlin added the hosts' second score three minutes later, with a fisted effort.
Paul Kerrigan and Tierney traded points to ensure a 0-03 to 0-01 scoreline after six minutes.
Conor Counihan's charges suddenly took firm command and hit a purple patch to register 1-04 without reply in a key six-minute spell.
O'Neill's first goal arrived the seventh minute after a move which was started by Paudie Kissane in defence.
The corner forward rifled a crisp shot past goalkeeper Eoin Culliton to move Cork 1-01 to 0-03 ahead - an advantage they would not relinquish.
Fintan Goold, Donncha O'Connor and Kissane added points to open up a 1-05 to 0-03 lead after 12 minutes. Cork were stringing together some clever moves at this stage, putting Laois under increasing pressure defensively.
Defender Kissane sent a 17th minute effort into the hands of Culliton after an attack involving nine different Cork players.
O'Loughlin was a key figure for the midlanders at centre-field, particularly during the opening period, and Munnelly soon broke Laois' 14-minute scoreless period.
Cork led 1-05 to 0-04 at this stage, with the Rebels putting together a run of three unanswered points as O'Neill and Goold both fired over.
Paul Cahillane nabbed a point back for the hosts, but Cork then upped the ante with another 1-03. There were points from Aidan Walsh (0-02) and Goold, before the Laois net was rattled for a second time.
Walsh fed O'Neill for his second goal in first half injury-time, with another smart finish giving Culliton no chance.
Laois manager Justin McNulty made a couple of notable changes at the interval with Damien O'Connor and Billy Sheehan withdrawn and Mark Timmons and Scott Conroy introduced.
Graiguecullen clubman Timmons moved into the full-back line with Peter O'Leary switching to left half-forward.
Cork suffered a setback when their strong-running midfielder Pearse O'Neill was dismissed four minutes into the second half.
The Aghada clubman added a second yellow card to the one he picked up for a trip on O'Loughlin in the 14th minute.
Laois were looking more effective at this stage and outscored their opponents by four points to one during the opening 13 minutes of the half.
Tierney (0-02), Colm Begley and O'Loughlin all landed points for the hosts to reduce the arrears to 2-12 to 0-09.
Colm O'Neill and Walsh replied with two excellent scores from play in a 40-second burst with Cork moving 11 points clear as the game entered the final quarter.
Laois battled on and with nine minutes remaining O'Leary forced Cork goalkeeper Alan Quirke to gather a pressure shot on his line.
But the Rebels' greater experience stood to them in the closing stages, and Laois could only add a consolation point late on as Tierney converted his fourth point - all from placed balls.
Scorers - Cork: C O'Neill 2-03, F Goold, A Walsh 0-03 each, D O'Connor 0-02, E Cotter, P Kissane, P Kerrigan 0-01 each.
Laois: MJ Tierney 0-04, R Munnelly, J O'Loughlin 0-02, P Cahillane, C Begley 0-01 each.
CORK: A Quirke; R Carey, E O'Mahony, E Cotter; N O'Leary, G Canty, P Kissane; A O'Connor, P O'Neill; P Kerrigan, F Goold, P Kelly; C O'Neill, D O'Connor, A Walsh.
Subs used: B O'Driscoll for Kerrigan, S Kiely for Canty (both 58 mins), L Shorten for D O'Connor, D O'Sullivan for Kissane, J Fitzpatrick for A O'Connor (all 66).
LAOIS: E Culliton; P O'Leary, K Lillis, C Healy; C Boyle, C Begley, C Boyle; K Meaney, J O'Loughlin; R Munnelly, P Cahillane, D O'Connor; MJ Tierney, A Kelly, B Sheehan.
Subs used: M Timmons for O'Connor, S Conroy for Sheehan (both half-time), S Ramsbottom for Kelly (46 mins), G Walsh for O'Loughlin, L Kealy for Strong (both 66).
Referee: Cormac Reilly (Meath)