Goalkeeping errors by Jake Cole gifted Shrewsbury two goals in three minutes as Barnet were beaten 2-1.
Cole made a brilliant point-blank save from Matt Harrold's header after half-an-hour but eight minutes later dropped a shot from Mark Wright to give Craig Disley an easy chance from six yards.
Then Cole was slow to get to a centre from Jake Robinson and Harrold had time to turn and fire in from six yards.
But Barnet, with only one away point this season, launched a second-half fightback.
The lively Mark Marshall had goalkeeper Chris Neal at full stretch then a flowing move ended with a crisp finish by left-back Jordan Parkes after 62 minutes.
As Barnet pressed for the equaliser Shrewsbury had a golden chance in stoppage time but with only Cole between three Shrewsbury players and the third goal the Bees keeper made amends by saving from Bolton Wanderers loanee Tope Obadeyi.
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