The Third Division outfit showed no ill-effects from their 4-0 drubbing at the hands of Chelsea in the FA Cup as they comprehensively beat their opponents at Gay Meadow.
Veteran striker Nigel Jemson put The Shrews ahead on 27 minutes and two minutes after half-time, Ryan Lowe put the hosts in command.
Prolific striker Rob Hulse handed the Second Division promotion-chasers a lifeline on 57 minutes before Lowe bagged his second on 70 minutes.
Dashing winger Luke Rodgers tightened his side's grip on the game with a fourth goal on 75 minutes.
Crewe forward Dean Ashton gave the visitors another glimmer of hope within the closing ten minutes but they were unable to deny Shrewsbury a final date against Carlisle.
