Kee opened the scoring with a 15th-minute free-kick which passed low through Dale's defensive wall in the League Two clash at the Pirelli on Boxing Day.
The striker was then instrumental as he turned provider for the hosts' second goal after 25 minutes, freeing Calvin Zola with a backheeled pass on the edge of the penalty area, allowing him to tuck the ball neatly past 'keeper Josh Lillis.
Rochdale got themselves back into it three minutes before half-time with a spectacular volley from Peter Cavanagh into the top corner of Dean Lyness' goal.
Burton then gifted the visitors an equaliser in the 54th minute, Nathan Stanton's poor back pass allowing Bobby Grant to nip past Lyness and roll the ball into an empty net.
But the Brewers regrouped and regained the lead again just three minutes later, Zola controlling the ball superbly and crossing from the right for Kee to dive and chest the ball over the line from four yards.