Luke Rodgers scored the only goal of the game as Kevin Ratcliffe's Shrewsbury got their season off to a winning start.
Rodgers, the Shrews' 22-goal top scorer last season, got off the mark for the campaign after 43 minutes.
He was put clear by skipper Nigel Jemson and cooly rounded Kevin Miller before sliding the ball home.
Exeter finished with 10 men after Brazilian newcomer Santos Gaia received his second booking in the 79th minute.
And the visitors, earlier denied an equaliser by Ian Dunbavin's fabulous save from substitute Steve Flack, proved the luck was against them when James Coppinger's 25-yard injury-time shot rebounded off the crossbar.
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