Shrewsbury grabbed their first league win against a 10-man Crewe side still seeking their first point.
Sean McAllister's glancing header from Lionel Ainsworth's cross put the home side ahead.
Crewe substitute Nick Powell was sent off for a studs-up challenge but Alex could have equalised when Max Clayton headed against the post.
Nicky Wroe wrapped up Town's victory with a brilliant solo run in stoppage time.
Crewe remain bottom of the Football League after their fourth straight defeat.
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Shrewsbury Town manager Graham Turner told BBC Radio Shropshire:
"That's a big relief. The confidence of getting our first win will make a difference to the players.
"We played some nice stuff going forward and we got ourselves into some good positions, but we've got to start getting on the end of some of these crosses.
"It's great to get our first win. We've got a week now where we can look forward to a good Carling Cup tie against Swansea."
Crewe manager Dario Gradi told BBC Radio Stoke:
"They got off to a good start but, by half-time, I thought we were back in the game.
"Nick Powell getting sent off obviously didn't help but we hit the post and took the game to them.
"The referee couldn't get the card out quickly enough. He didn't stop to think about it."
Shrewsbury 25 Smith 02 Grandison 03 Jacobson 05 Sharps 06 Cansdell-Sherriff 04 McAllister 07 Wright 08 Wroe 16 Ainsworth (Richards - 89' ) 10 Morgan Booked 24 Gornell (Collins - 82' Booked ) Substitutes 01 Neal 12 Hazell 11 Leslie 14 Richards 09 Collins Crewe Alexandra 01 Phillips 03 Davis 05 Artell 06 Dugdale 15 Martin 04 Westwood Booked 07 Bell (Clayton - 70' ) 08 Murphy 09 Miller 10 Leitch-Smith 11 Moore (Powell - 60' Dismissed ) Substitutes 13 Martin 12 Shelley 24 Hughes 19 Clayton 25 Powell