In an open and attacking affair both sides had chances to break the deadlock in the first-half.
Nathan Baxter was twice on hand to produce smart stops, whilst Rhys Browne and Alex Fisher almost netted at the other end as it remained goalless.
The second half proved to be a similar affair with both sides failing to make the most of chances to break the deadlock before Tom James stepped up to win it in the 96th minute with an unstoppable free-kick.
Looking to end a 12-game winless streak against the Cumbrians, Darren Way made two attacking changes by replacing the wingers.
Bradford loanee Omari Patrick was handed a first league start in place of Jake Gray whilst Browne swapped places with Yoann Arquin wide on the left.
On a crisp October afternoon the Glovers started in positive fashion, before a head injury suffered by Alex Pattison caused a lengthy delay that swung momentum back in favour of the hosts.
With Town playing with 10-men whilst the Middlesbrough loanee received treatment off the pitch, Macauley Gillesphey forced Baxter into a smart early save with his rasping effort from 25 yards.
Surviving the period with a numerical disadvantage the visitors had two chances of their own in quick succession.
Browne, who looked determined to justify his inclusion, breezed past Jack Sowerby on the left before his shot destined for the near post was deflected behind for a corner.
The lively winger was at the heart of the action again just two minutes later, ghosting past two Carlisle defenders to burst into the box only for his curling effort to fly just over the bar.
Becoming breathless stuff in Cumbria, John Sheridan’s side were next to go close when Mike Jones’ deflected shot from inside the box was well palmed away by Baxter, as the chances continued to flow.
In an otherwise promising start for the Glovers they were dealt a blow just before the half-hour mark when Pattison – still feeling the effects of his early head injury – trudged off to be replaced by Jake Gray in a like-for-like swap in the middle of the park.
Losing its intensity following the substitution the game burst back into life with chances at both ends 10 minutes before the break.
Firstly, Gary Liddle had a bobbling shot from a corner cleared off the line by the freshly introduced Gray whilst at the end, Fisher had an audacious lobbed-attempt acrobatically saved by Adam Collin to keep the score at 0-0.
Faced with six minutes of additional time due to a stop-start opening 45 minutes the hosts enjoyed the final spell of pressure but a resolute-looking Town defence stood firm to keep it even at the halfway stage.
With the temperature plummeting in the north of England Baxter maintained his hot form in Cumbria just two minutes after the restart, brilliantly getting down to his right to push Ashley Nadesan’s shot around the post as the second half started quickly.
Buoyed by their encouraging start Carlisle remained on the front foot but faced by a strong Yeovil defence, couldn’t capitalise as the green and whites grew into the half.
A weaving Jake Gray run ended with a shot straight at Collin prior to a meandering Browne run ending with a shot just off target on 63 minutes.
Sensing the opportunity to take all three points the diminutive Wes McDonald was introduced for his first action in two months following injury, replacing Patrick on the wing as the visitors remained ultra attacking.
Enjoying plenty of early touches after coming on the tricky winger provided another outlet for Town, but chances dried up for both sides in the final quarter of the game.
In a final flurry, both sides threw caution to the wind and pressed for a late winner but it was the green and whites who prevailed.
In the sixth minute of stoppage time McDonald won a free-kick on the left of the box and from the unlikeliest of angles, James dispatched a drilled strike past Collin to send the away end into raptures and ensure all three points would be returning to Somerset.
Carlisle United: Collin; Sowerby, Gerrard, Liddle, Gillesphey; Yates (Bennett 71′), Etuhu, Slater (McCarron 80′), Jones; Campbell (Devitt 60′), Nadesan.
Subs not used: Gray, Grainger, Glendon, Miller.
Yeovil Town: Baxter; James, Mugabi, Donnellan, Dickinson; Patrick (McDonald 66′), D’Almeida, Pattison (Gray 29′), Browne; Olomola, Fisher (Arquin 80′).
Subs not used: Nelson, Mahmutovic, Santos, Rogers.