On-loan striker Leon Best sealed a remarkable second-half revival by Yeovil with a double strike.
Joe Garner put Carlisle ahead in the 43rd minute when he powered home a 12-yard volley from Kevin Gall's cross.
But Yeovil were a different side after the break with Best setting up the equaliser for substitute Wayne Gray.
Best headed Yeovil into a 72nd-minute lead and made the game safe with a 25-yarder before setting up Chris Cohen, who smashed into the top corner.
Carlisle: Westwood, Raven, Murphy, Livesey, Aranalde, Gall (Johann Smith 75), Murray (Holmes 75), Joyce, Jeff Smith, Garner, Hawley.
Subs Not Used: Williams, Gray, McDermott.
Goals: Garner 43.
Yeovil: Mildenhall, Lindegaard (Tonkin 41), Skiverton, Forbes (Guyett 46), Jones, Best, Cohen, Kalala, Sweeney, Davies, Stewart (Gray 45).
Subs Not Used: Brittain, Welsh.
Booked: Jones, Cohen, Tonkin, Kalala.
Goals: Gray 49, Best 72, 90, Cohen 90.
Ref: E Ilderton (Tyne & Wear).