Sean Devine went from saint to sinner after scoring the opener but missing a penalty in a tense battle.
Exeter had the best chance in a scrappy opening when Justin Walker burst into the box and flashed a shot across the face of goal.
Steve Flack broke down the right in the 15th minute and his dangerous ball into the box was almost tapped into his own goal by Peter Wilding.
Walker thumped a long-range effort well over the bar but the deadlock was eventually broken in the 18th minute.
Martin Thomas found Flack on the edge of the box and he rolled the ball to Devine. The master marksmen beat a defender before drilling a low shot into the bottom corner.
Devine went close with a fine strike from the edge of the box after good work from Scott Hiley, but his effort was superbly stopped by Ian Dunbavin.
It took more than half an hour for Shrewsbury to have a shot on target, and Jamie Tolley's weak volley at the far post hardly troubled Kevin Miller.
After the break Dave Artell met Leon Drysdale's cross for the visitors but he headed into the arms of the goalkeeper.
Shrewsbury pulled level nine minutes after the restart when referee Lee Cable accepted the advice of his assistant and signalled for a penalty after Adrian Whitbread was adjudged to have handled Tolley's cross. Nigel Jemson calmly converted the spot-kick.
Devine attempted to respond, curling a free-kick inches over the bar before drilling a shot into the arms of the goalkeeper.
Devine should have put the home side ahead again when Wilding handled in the area but the striker blasted the penalty over the bar.
Exeter boss Neil McNab said afterwards: "I am very disappointed because this was two points dropped. It was about two penalties and two average looking teams."