The visitors were heading to their first away win for eight months until Simpson fired his second goal of the game from 15 yards nine minutes from time.
Yet the Shrews could have snatched victory in stoppage time but substitute Tom Bradshaw missed from four yards following a cross from Paul Parry.
Simpson gave Crawley an ideal start with a first-minute goal, firing home from 20 yards to the left of keeper Chris Weale.
But Shrewsbury hit back to level after 14 minutes through a cool finish from skipper Matt Richards.
John Taylor then put Shrewsbury ahead with a superb goal in the 34th minute. The midfielder ran through the centre before beating Paul Jones with a powerful shot.
Crawley keeper Jones saved well to deny Luke Rodgers before Simpson secured a point.