Mayo had three points to spare over a disappointing Laois side in Sunday's All-Ireland Football Championship quarter-final at Croke Park.
Mayo's Kieran McDonald holds off Padraig McMahon of Laois
Mickey Moran's Connacht champions will now face the Leinster title winners Dublin in the semi-final on 27 August.
The defeat brought an end to veteran manager Mick O'Dwyer's stint in charge of the Laois panel.
Ross Munnelly landed five points for Laois but Conor Mortimer also got five for Mayo who led from start to finish.
"I am proud of my players. They had the hunger and they had the passion too," said winning boss Moran.
"We said at half-time we wanted to stay ahead no matter what it took.
"We have a match next week and it will take an almighty effort, but we are through and we are delighted.
"People will make Dublin favourites - they will not give us a chance."
Mao: D Clarke; D Geraghty, D Heaney, K Higgins; A Higgins (0-02), J Nallen, P Gardiner; R McGarrity (0-01), P Harte; BJ Padden (0-01), G Brady (0-01), C McDonald (0-01); A Dillon (0-02 (0-01f), C Mortimer (0-05 (0-03f)), M Conroy.
Substitutes: P Kelly for Heaney (23-27 mins, 67-70, blood sub), A Kilcoyne (0-01) for Padden (28), K O'Neill for Conroy (29), B Regan for O'Neill (44), A Moran for Brady (57).
Laois: F Byron; A Fennelly, D Rooney, J Higgins; P O'Leary, T Kelly, P McMahon; P Clancy (0-01), B Quigley; R Munnelly (0-05 (0-04f)), C Conway (0-02 (0-02f)), B McCormack; B McDonald (0-02), N Garvan, B Sheehan.
Substitutes: D Brennan (0-01) for McCormack (27 mins), I Fitzgerald for Quigley (51), G Kavanagh for Sheehan (54), P Lawlor for McDonald (63).
Referee: Joe McQuillan (Cavan).