Jordan Cook and Liam Noble were also on target for the home side with Liam Sercombe replying for the Grecians, who went down to their ninth successive away defeat.
Exeter's Daniel Nardiello and Nooble both his the woodwork before two goals inside 60 seconds. First
Zoko grabbed his 13th of the season for Carlisle, drilling the ball past Exeter goalkeeper Lenny Pidgeley after working a neat one-two with Cook on the edge of the area.
Sercombe forced home Billy Jones's cross from the left from close range a minute later, but their lead only lasted six minutes before Cook scored with a clever lob from a difficult angle in the 42nd minute.
Carlisle added to their lead in the 51st minute when Jon-Paul McGovern's cross from the right was shielded by Zoko, who laid the ball back to Noble who drove his shot home from 12 yards.
The action came thick and fast. Two minutes later Exeter won a penalty after Collin had impeded Alan Gow, but Nardiello fired his spot kick against the crossbar before Zoko beat two defenders and slammed a shot past Pidgeley from 18 yards in the 77th minute.