Drew Talbot had given the Spireites a 16th-minute lead but after Parker had headed home from a corner Zoko took advantage of weak defending to race away and win it for Carlisle with his 10th goal of the season.
Chesterfield mastered the tricky surface much the better in the opening period and took the lead when Talbot twisted and turned before getting in a shot from eight yards which squirmed through keeper Adam Collin’s grasp and just crept over the line.
Spireites boss John Sheridan sent on sub Nicky Ajose in the 59th minute and he immediately posed a threat, nipping between two defenders to slide his shot past Collin but just wide of the right-hand post.
But it was Leeds loanee Parker, making his home debut for Carlisle, who headed the home side level with a quarter of an hour remaining, getting on the end of Jon Paul McGovern’s corner to guide the ball past keeper Tommy Lee from six yards.
Carlisle grabbed the lead in the 84th minute courtesy of an error by James Hurst whose underhit backpass was seized on by Zoko. The striker rounded keeper Lee before slipping the ball home from eight yards.