The match was being played on neutral turf as Carlisle used Bloomfield Road as their temporary home due to floods in Cumbria.
The Cumbrians took the lead through Danny Grainger’s 25th-minute free kick and Yeovil almost levelled moments later as Tahvon Campbell’s close range effort was saved and Liam Walsh’s follow-up went wide.
Town levelled with 19 minutes remaining of the tie when Francois Zoko headed past Dan Hanford to net against his former club.
Carlisle retook the lead when centre-back Mark Ellis nodded in from six yards but Shaun Jeffers took things to a replay with a low shot in the 93rd minute.
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