The Jazz were trailing 77-76 with 1:15 remaining when Gordon Hayward found Derrick Favors on a baseline pass for a go-ahead slam dunk.
The Bobcats misfired on the ensuing possession and Burke then helped seal the outcome with a driving layup as the shot clock expired for an 80-77 lead.
Charlotte's Al Jefferson missed an open 3-pointer and Utah followed with 3-of-4 free throws to wrap up a second win in three games.
Alec Burks provided 14 points and Marvin Williams logged a double-double of 13 with 10 rebounds.
2014: The Year in Music [PHOTOS]