Ruairi Russell gave the winners an early boost when goaling after six minutes and he struck for a second goal 12 minutes later.
Laois gained some hope when Colm Miller converted a penalty after Daryl Fay was fouled but Meath led by 2-7 to 0-3 at the break.
Nine minutes after the restart Meath’s Alan Fox finished a Stephen Bray sideline to the net. Laois’ woes were added to when Gerry Nerney was shown a red card following a high challenge on Cathal Sheridan Bray and Willie Byrne added goals and full back Trevor Bannon and centre back Fergus McMahon got among the point scorers for the winners.
Scorers : Meath: R Russell 2-1, S Bray 1-3, A. Fox, W. Byrne 1-1 each, C Sheridan 0-4, B Lynch, F McMahon, T Bannon, G Rogers 0-1 each.
Laois: C. Miller 1-2, D Fay, T Gee, G. Nerney, M. Malone 0-1 each.
MEATH: J Curry; C McLoughlin, T Bannon, P Nugent; N Horan, F McMahon, B Kieran; I McManus, J Gallagher; C. Sheridan, W Byrne, S Bray; A. Fox, B Lynch, R Russell.
Subs - P Murray for McManus, G Lynch for Curry, G Rogers for Murray, S Smith for McLoughlin, P Duff for B Lynch.
LAOIS: D O’Mahoney; M O’Connell, R Hayden, T Mulligan; D Brennan, M Malone, D Bolton; B Fitzpatrick, A Deegan; B O’Connor, C Miller, M Rooney; D Fay, T Gee, G Nerney.
Subs - D O’Hara for Brennan, D Hogan for Hayden, B Fennell for O’Connor, J Kavanagh for Gee, T White for Fay.
Referee T. Quigley (Wexford).