Shrewsbury captain Ben Davies struck a last-minute winner as his side reached the second round of the Johnstone's Paint Trophy at the expense of Exeter.
The Grecians fell behind when Michael Symes teed up Kevin McIntyre, who rolled the ball in from 15 yards.
Exeter equalised when a Ben Watson cross came back off the upright and from a narrow angle, Ryan Harley drilled into the left corner.
Davies capitalised on a poor punch by keeper Paul Jones to grab the winner.
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