Utah is now 9-13 in games Burke has played and 1-11 with him out of the lineup.
Former Jazz center Al Jefferson had 18 points and 10 rebounds in his return to Salt Lake City, but shot just 8 of 23 from the field.
Jefferson received a warm ovation from the fans in attendance and embraced Jazz CEO Larry Miller. Jefferson left Utah in free agency over the summer to signed a three-year, $41 million contract with Charlotte. Jefferson averaged 18.5 points and 9.5 rebounds in three seasons with the Jazz.
After the Bobcats took the league with 1:15 remaining, Burke scored on a layup before the shot clock buzzer to put the Jazz up by three.
With 19 seconds left, Favors blocked a layup by Ramon Sessions, but Sessions got the ball back and found a wide open Jefferson behind the 3-point line, who missed the game-tying 3-pointer. Jefferson would later make a desperation 3-pointer at the final buzzer.
Gerald Henderson led a struggling Bobcats offense with 19 points and Kemba Walker added 18. Charlotte shot just above 36 percent from the field and were held to just 15 free throw attempts. The Bobcats are now 10-12 in games decided by single digits.
Charlotte has lost three in a row and four of their last five. The Bobcats have three games remaining on their Western Conference road trip, including a back-to-back against the Los Angeles Clippers and Portland Trail Blazers. The Bobcats are 0-4 on the road against the West and 2-8 overall.