Donal Burke bailed Dublin out again with a thrilling 0-13 haul - but boss Mattie Kenny admitted they lived desperately dangerously.
His Blues were left clinging on for a two-point win having led by seven with 68 minutes on the clock.
Alex Considine’s 62nd minute goal ultimately separated the sides with the sub netting in his very first involvement.
Fellow sub Paul Crummey struck a vital point too, Dublin’s last of the game, in the 68th minute.
From there on it was all Laois and Cheddar Plunkett’s side gave the hosts a real run for their money with 1-2 in the closing stages at Parnell Park.
James Keyes and free-taker PJ Scully both pointed either side of a goal from goalkeeper Enda Rowland who smashed a free to the net.
Kenny sighed: “We left Laois in that game right up until the death and that’s an area we absolutely have to improve on in the coming week.”
Dublin scorers: D Burke (0-13, 7f), A Considine (1-0), F Whitely (0-3), J Madden (0-1), C Crummey (0-1), R Hayes (0-1), P Crummey (0-1).
Laois: PJ Scully (0-8, 5f, 1 s/l), E Rowland (1-2, 1-2f), M Dowling (1-0), J Keyes (0-2), C Dwyer (0-1), R King (0-1), A Corby (0-1).
