It took Kee only 10 minutes to find the net from 10 yards after a crisp exchange of passes with fellow striker Calvin Zola inside the box.
Accrington looked much the brighter team in the first half, but Burton had chances to increase their lead in a burst of pressure.
Skipper Zander Diamond could only poke a Kee flick straight at goalkeeper Paul Rachubka and the defender also heading narrowly wide after stealing on the end of a Chris Palmer free-kick.
Kee also went close with a 15-yard shot, while Stanley were unable to turn their superior possession into scoring opportunities.
After the break, Burton goalkeeper Dean Lyness had to back-pedal to tip a huge clearance from his opposite number over the crossbar and also did well to push a skidding Luke Joyce shot round a post.
Zola had a chance to increase Burton's lead, but was denied by Rachubka's one-handed save.