Left-back Charles Dunne was sent off early in the second half for Wycombe, who grabbed a late goal through Matt McClure.
Dunne had a low shot saved by Jordan Pickford early on while Damien McCrory rasped a 20-yard drive wide of the home side's post.
But Kee produced a touch of class on 27 minutes, chesting down the ball just outside the box before spinning and firing into the right-hand corner.
It was to be an uphill task for Wycombe soon after the restart as Dunne hacked down Burton right-back Phil Edwards in the 47th minute and earned a second yellow card.
And just five minutes later Gary Doherty brought down Kee in the box, who stroked in the resulting penalty.
Kee nearly grabbed his hat-trick 20 minutes from full-time - forcing a superb save from Matt Ingram - before McClure's low finish gave the Chairboys a 90th minute consolation.