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Shrews keeper Chris Neal seemed to have the shot covered but found Wotton's strike too hot to handle and fumbled the ball over the line in the 21st minute.
Wotton - who left the field injured injured in the 86th minute - could have made it 2-0 after half-time with a thunderous strike from the edge of the box which Neal did well to palm over.
Shrews striker Marvin Morgan, who missed a golden opportunity in the first half, looked to have atoned when he swept past Argyle keeper Jake Cole but central defender Darren Purse did well to clear the danger in a frenetic last 20 minutes.
Neal was beaten again in the 75th minute but substitute Alex MacDonald's rising drive from the edge of the area came back off the post.
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