Kee celebrated his return to the starting line-up by heading the Brewers level after David Clarkson had grabbed his third goal of the season for Rovers.
Clarkson brought a dull first-half to life by giving Rovers the lead in the 30th minute. Burton struggled to deal with on-loan striker Tom Eaves in an aerial battle and the ball broke loose for the midfielder to drill a low shot into the bottom corner from the edge of the area.
The home team threatened an equaliser in a spell before half-time but Kee twice had shots saved by Neil Etheridge, while efforts from Jacques Maghoma and Justin Richards missed the target.
Burton goalkeeper Stuart Tomlinson had to produce a flying save to deny Oliver Norburn after the break, but the hosts came back to level the scores in the 50th minute when the unmarked Kee nodded home a Lee Bell free-kick from six yards.
Cleveland Taylor had a chance to put Burton in front in the 71st minute but blazed his shot wide after breaking clear.