After serving up an exciting league clash in Navan, both sides found their efforts to be in vain as relegation was their reward as Clare survived by virtue of their surprise success in Sligo.
While the victory for Laois, who have had a lot of problems in their camp lately, will give them a boost for the championship, it is the opposite scenario for Meath who had serious problems at midfield and in the centre of their defence.
Ian Fitzgerald and converted wing back Colm Parkinson took advantage of the home side's lack of composure in the heart of the rearguard as they got the better of Nigel Nestor and Darren Fay.
Another of Meath's All-Ireland winners, corner back Colm Murphy, was shown a straight red card after opposing wing forward Shane Cooke went down 10 minutes after the change of ends.
As well as the concession of a man, Meath gave away too many frees in the danger zone and Laois profited with Fitzgerald and Chris Conway sharing eight converted frees.
The sides were level five times in the first half and Laois led by 16 to 1-5 at the break.
The goals came after 11 and 17 minutes with Fitzgerald racing through the middle to find the net and Meath's top scorer Graham Geraghty levelling with a tap in following a flick by Ollie Murphy.
It took Meath 18 minutes to get on the mark in the second period with Geraghty converting a free awarded for a foul on himself.
They were three points behind with six minutes left and, although Murphy and Trevor Giles reduced the arrears to the minimum, Conway converted his fifth free to steady the Laois men before Geraghty closed the scoring.
LAOIS: F Byron; A Fennelly, P McDonald, P Leonard (0-1); D Brennan, P Conway, J Higgins; J Kealy, N Garvan; S Cooke (0-1), I Fitzgerald (1- 3), P Clancy; K Kelly, C Parkinson, C Conway (0- 6). Subs: B McDonald for Cooke, E Delaney for P Conway, D Sweeney for Kelly.
MEATH: C Sullivan; M O'Reilly, D Fay, C Murphy; P Shankey, N Nestor, H Traynor; N Crawford, A Moyles; E Kelly, R Kealy (0-2), D Curtis (0-1); O Murphy (0-1), G Geraghty (1-4), T Giles (0-2). Subs: N McKeigue for Kelly, E McManus for Curtis, R McGee for Traynor.
Referee: M McGrath (Donegal).