Jordan Rhodes hit a hat-trick in 29 first half minutes to wrap up a victory for Brentford which keeps them second.
The on-loan Ipswich striker volleyed a spectacular right-foot opener over his own shoulder after just 90 seconds.
He capitalised on a poor backpass by Kelvin Langmead to score the second with his left foot before heading the third from Adam Newton's cross.
Grant Holt pulled one back from Graham Coughlan's flick, his 21st this season, but Town drop out of the play-off zone.
Shrewsbury: Daniels, Darren Moss, Langmead, Coughlan, Ashton, Humphrey, Dunfield, Murray (Pugh 46), Davies, Holt, Walker (Hibbert 46). Subs Not Used: Jackson, Leslie, Chadwick.
Booked: Ashton.
Goals: Holt 68.
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Booked: O'Connor.
Goals: Rhodes 2, 17, 29.
Att: 5,674
Ref: Anthony Taylor (Greater Manchester).
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