Burke, who finished with 20 points overall, drained a go-ahead 3-pointer with 2:38 remaining and later added a pair of foul shots to secure the win for the Jazz.
Gordon Hayward contributed 12 points and 10 rebounds as Utah improved to 2-2 on a five-game road trip.
Al Jefferson supplied 19 points and 11 rebounds for Charlotte, which had its three-game winning streak snapped.
Kemba Walker struck for 20 points, five rebounds and four assists.
Celebrity Couples of 2014 [PHOTOS]