The home side put County under pressure early on with keeper Bartosz Bialkowski called into action on several occasions.
Bialkowski comfortably saved Michael Doyle's shot and did well to keep out Ryan Flynn and Paul Gallagher.
After Blackman fired against a post, Kitson scored with a firm header from Flynn's cross in the 50th minute.
United keeper Mark Howard made a fine save to keep out Francois Zoko's header before County equalised in the 76th minute. The ball came back off the crossbar following a goalmouth scramble, Jeff Hughes played the ball back across the face of goal and namesake Lee tapped in at the far post.