Laird headed home into the bottom corner from Jon Ashton's flick-on in the 87th minute.
Crewe will feel aggrieved to have ended up empty-handed after Clayton Donaldson forced a fine save from Stevenage goalkeeper Chris Day on the stroke of half-time and Byron Moore hit the post with his shot from inside the penalty area just after the hour.
Laird's late strike ended Boro's six-game winless streak but the match looked to be heading for a draw after the visitors dominated possession in a drab first half but failed to carve out any openings bar high and wide efforts from David Bridges and Craig Reid. Crewe were restricted to a 40-yard shot from Danny Shelley which flew inches wide.
The youngster then had the Alex's first effort on target after 33 minutes but his daisy-cutter was easily held by keeper Chris Day.
Source: PA
Source: PA