Crawley should have taken an early lead when Billy Clarke was expertly picked out by a fine pass from Kyle McFadzean, but lifted his shot over the crossbar with only goalkeeper Joe Anyon to beat.
Shrewsbury had that sinking feeling again when Crawley edged ahead in the 24th minute.
Clarke's free-kick struck the wall and Josh Simpson reacted quickest to drive in the loose ball with a low shot from 12 yards.
The home side were out of luck when Miles Storey pounced on a defensive error only to see his shot come back off the inside of a post.
But the equaliser arrived in the 56th minute when winger Paul Parry bent home a fine shot from 15 yards for his fourth goal of the season.
Parry then cracked a long-range shot against a post as Shrewsbury chased a winner, but the hosts were indebted to a fine fingertip save from goalkeeper Anyon which denied Jamie Proctor and the points where shared.