The Cumbrians were on top from the first minute and should have taken the lead on several occasions but always found Yeovil captain Terrell Forbes a rock at the heart of their defence. Carlisle's pressure should have told on 24 minutes when Danny Livesey had a great chance but instead volleyed into the ground, and Smith could only divert the resulting header off target from close range.
On 38 minutes Yeovil took the lead against the run of play when they broke quickly following another Carlisle corner. Veteran Marcus Stewart teed himself up nearly 35 yards out and let fly with his left foot. His drive looked comfortable for keeper Keiren Westwood until it flicked off Livesey's head and looped over the wrong-footed shot-stopper.
Seconds after the break the visitors' on-loan keeper Asmir Begovic saved dramatically at his near post from Peter Murphy's header but, with 14 minutes to play, Murphy made up for the miss with a lucky equaliser. The defender met Marc Bridge-Wilkinson's deep corner with a stooping header that ricocheted off the unfortunate Stewart and past the prone Begovic.
With the home side going in search of a late winner teenage striker Gary Madine was sent on for the final push. And with his first touch, deep in the visitors penalty area, he chested down midfield schemer Bridge-Wilkinson's lofted cross allowing the on-rushing Dobie to fire in and send the home fans wild with delight.