Two goals from the 6ft 5in marksman and a Joe Garner header handed the Cumbrians their first win in six League One games at a drenched Huish Park.
The visitors took the lead after 21 minutes when Matty Robson's drilled cross was bundled home at the far post by the stretching Beck. The lively Blues came close to doubling their advantage before the break, with Beck and David Symington twice denied by Yeovil goalkeeper Marek Stech.
Only 50 seconds into the second half Carlisle scored a deserved second when 18-year-old Beck lashed a stunning left-footed volley into the top corner from 20 yards.
On-loan striker Garner twice came close to extending the visitors' lead even further, before substitute Reuben Reid gave the disappointing hosts a glimmer of hope.
However, Garner clinically struck on his third opportunity with a smart header - securing a welcome three points from his side's 317-mile trip to Somerset.