Carlisle dominated the first-half but struggled to find their finishing touches.
It had been a frustrating afternoon for the Cumbrians against a Glovers side that defended doggedly after grabbing a first-half lead through Marcus Stewart’s 28-yard effort.
The goal came against the run of play in the 38th minute and was a classy individual effort by Stewart, who fired past Kieren Westwood into the top left-hand corner.
Carlisle’s attacking was rewarded when Marc Bridge-Wilkinson’s corner from the left was headed home by Peter Murphy – the ball cannoning off a defender as it flew past Asmir Begovic.
Sub Gary Madine then chested down Bridge-Wilkinson’s cross and Dobie volleyed in from 10 yards.