Kee atoned for a penalty miss at Oxford a week earlier by putting Burton in front from the spot in the 21st minute after Dominic Knowles had been tripped in the area by Dons skipper Alan Bennett.
The Burton striker might have doubled the lead six minutes later, but his overhead kick dropped onto the roof of the net.
With the hosts on top, goalkeeper Ross Worner came to the visitors' rescue in the 33rd minute when he kept out a Jimmy Phillips shot.
Dons substitute Charlie Wyke had a chance to make an immediate impact after the restart but twice headed too high.
Burton also had more opportunities, with Kee heading narrowly wide and substitute Matty Palmer firing straight at Worner, who also tipped over a Damien McCrory shot.
Dons went close when Jack Midson hit a post before Jones's dramatic equaliser.
- Sports & Recreation
- Darren Jones
- Billy Kee