The on-loan Leicester striker had only been on the pitch six minutes when fellow substitute John Miles threaded a ball through and Kee finished well from 10 yards out on 70 minutes.
And he made it nine goals for the season at the death when he got on the end of Ian Dunbavin's long punt, raced forward and, although Tommy Lee got a touch, the ball rolled into the net.
The defeat extended the Spireites winless run to six matches and leaves them having to win their last match and hoping other results go their way.
Dunbavin had earlier pulled off three superb saves to keep out Ishmail Demontagnac from close range and push out his 25-yard effort while he also stopped Drew Talbot's effort sneaking into his near post.
But Chesterfield keeper Lee also had to be alert to push out a Bobby Grant lob. However, he could do nothing about Kee's double, which makes it two wins out of two for mid-table Stanley.