Luke Guttridge was the Aldershot hero after his goal gave them their first win in over a month at the expense of promotion hopefuls Shrewsbury.
Visiting keeper Chris Neal saved well from Aaron Morris' fierce volley before Nicky Wroe forced Jamie Young into action at the other end.
Adam Smith's cross hit the post for the Shots and Mark Wright ballooned over for the Shrews.
Guttridge grabbed the winner from close in from Danny Hylton's pass.
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Aldershot boss Dean Holdsworth told BBC Surrey:
"The desire and passion we showed was outstanding. We raised the bar. We played against a very good side who are arguably one of the title favourites.
"Man for man, it was fantastic. They were giving everything for each other and the shirt. That's what I expect, and what we want.
"We've had a run of games where we were punished for our mistakes. I'm delighted we got our rewards for working extremely, extremely hard."