Laois opened the scoring within a minute as Willie Dunphy fired over.
Westmeath responded strongly, hitting three points in a row to take the early initiative, the pick of them coming from Niall Mitchell.
The visitors were looking the more threatening but Cha Dwyer and King (free) managed to haul Laois back on level terms at 0-4 each after 17 minutes.
Paddy Whelan’s goal put Laois ahead after that, but Westmeath again responded well to going behind, hitting four in a row to go back in front.
Laois needed to get something going before the break, and two excellent points from Picky Maher helped them draw level at the interval (1-8 to 0-11).
The hosts took control in the second half, and a run of eight points in a row appeared to see them safely over the line.
However, a goal from Robbie Greville set up a grandstand finish, as points from Ross King and Aaron Dunphy kept Laois in front.
Eoin Price then got a second Westmeath goal but a late King free saw the home side over the line in the end.
R King 0-10 (8f, 65), S Maher 0-4, A Dunphy 0-3, P Whelan 1-0, C Dwyer 0-2, W Dunphy, C Taylor, E Rowland (free) 0-1 each.
A Devine 0-5 (3f), N Mitchell 0-4, R Greville 1-1, E Price 1-0, P Greville 0-2 (1f), G Greville, S McGovern, C Boyle, D McNicholas, J Galvin 0-1 each.
E Rowland; C Healy, L Bergin, D Palmer; C Collier, C Dwyer, L Cleere; R King, P Purcell; C Taylor, A Corby, B Conroy; W Dunphy, S Maher, P Whelan.
A Dunphy for Corby (29), M Whelan for Taylor (42), S Downey for Conroy (48), E Lyons for Dwyer (61), S Bergin for P Whelan (65).
P Maloney; C Shaw, T Doyle, T Gallagher; G Greville, P Greville, J Boyle; A Clarke, C Boyle; A Devine, D McNicholas, N Mitchell; S McGovern, R Greville, K Doyle.
D Egerton for J Boyle (56), N O’Brien for McGovern (57, J Galvin for C Boyle (66).
J Owens (Wexford).
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