Zoko lifted his shot over goalkeeper Sam Johnstone to earn the Cumbrians their fifth away win of the season and step up their top-six challenge.
It was no more than the visitors deserved after dominating the first half and hitting the woodwork three times. That came after Scunthorpe, with only one win in their previous 11 games, took a fourth-minute lead when winger Andy Barcham curled a shot in to the top far corner from an acute angle for his sixth goal of the season.
But with the home defence wobbling, Carlisle twice came close to a quick equaliser through two headers from leading marksman Lee Miller. Each effort came back off the woodwork and the Cumbrians were denied again when Peter Murphy rattled the crossbar after an error by young keeper Johnstone.
Skipper Paul Thirlwell then had a shot deflected inches wide as the visitors, without a goal in their previous three away games in the league, piled on the pressure without having any luck again in front of goal. Carlisle were finally rewarded with a 64th-minute equaliser when midfielder James Berrett broke unchallenged into the box to drill a low shot into the far corner.
Scunthorpe might twice have snatched a winner with substitute Jimmy Ryan and skipper Sam Togwell both missing golden chances with the goal at their mercy. But with the game in stoppage time, it was Zoko who won it for Carlisle.