The Cumbrians looked a well-beaten side until Lee Miller struck from six yards in the 90th minute before Yeovil defender Luke Ayling scored an own goal deep into added time.
Kevin Dawson had given Glovers a first-half lead before Miller equalised just before the break.
Former Carlisle striker Paddy Madden grabbed his 21st goal of the season after the interval and James Hayter added a third for Yeovil before Carlisle's late fightback.
There was an early scare for Yeovil when Miller broke through and pushed the ball past visiting goalkeeper Marek Stech. The two players collided, but referee Geoff Eltringham waved away Carlisle's penalty pleas.
Sam Foley scooped a close-range chance over the crossbar before Yeovil took a 25th-minute lead when Madden played an astute ball inside to Dawson, who made progress into the penalty area to smash a 15-yard shot high into the roof of the net.
Carlisle levelled in the 39th minute when Mark Beck headed on Jordan Mustoe's free-kick and Miller was sharpest to react, poking a right-footed shot low between Stech's legs from the six yards.
Madden restored the Glovers' lead in the second half, tapping in from six yards after goalkeeper Adam Collin had parried Ed Upson's shot.
It looked all over for Carlisle when Hayter made it 3-1, finding space behind the defence to calmly slide the ball past Collin from inside the area.
But there was drama to come when, almost on full time, Miller controlled David Symington's ball into the box before firing low into the right hand corner from six yards and with seconds remaining Carlisle's French substitute Mathieu Manset, who only received international clearance hours before the game, saw his shot blocked only for Ayling to turn the ball into his own net.