Yeovil twice equalised before Zoko managed to force the ball home in a goalmouth scramble to earn the home side three points.
Lee Miller had given Carlisle a first-half lead from the penalty spot his 11th of the season, but Jon Obika levelled straight after the break before Paddy Madden restored Carlisle's advantage.
A late strike from substitute Dominic Blizzard then looked to have earned Yeovil a share of the spoils only for Zoko to twist and turn inside the area before squeezing home the winner.
Carlisle achieved the breakthrough in the 33rd minute when Jon Paul McGovern's cross was handled by Bondz N'Gala and Miller slammed the spot kick high into the net, but Yeovil were back on terms within a minute of the restart when Obika found space to the left of goal to drive home a firm shot at the near post.
Two minutes later Carlisle were back in front with a first league goal for Irish striker Madden, who ran through to slip the ball wide of the advancing Walker before Blizzard and Jonathan Grounds combined for Yeovil's second equaliser in the 81st minute.