Top scorer Grant Holt crashed home his 23rd goal of the season from the penalty spot five minutes after the break to put the home side ahead.
It looked like being enough to secure all three points for Paul Simpson's men but in the 83rd minute Marcus Stewart levelled for the visitors to ensure they made the long trip home with a point and still holding down a play-off place.
Despite creating few clear-cut opportunities, the South coast side were left to rue one obvious chance that went begging - when a first-half spot kick from Matt Gill smashed against the Shrewsbury crossbar and rebounded to safety.
Shrewsbury made all the early running and Exeter keeper Paul Jones had to be alert to tip over a Holt header but, with their first significant attack, the visitors should have taken the lead.
Midway through the half, Shrewsbury centre-back and skipper Graham Coughlan was adjudged to have handled a Steve Basham shot but Gill blasted the resulting penalty against the woodwork.
The home side responded by dominating the remainder of the first half, but were denied a breakthrough until the 51st minute - and when Moses Ashikodi was sent sprawling in the Exeter box, Holt made no mistake from the penalty spot to put Town ahead.
With only one away win all season Shrewsbury seemed on course to record their first double of the season but paid the price for a lapse in defensive concentration seven minutes from time, allowing Stewart to nod home from inside the six yard box.