The Bulls broke a 104-all tie with 25 seconds left on a 15-footer from Butler and a pair of free throws by McDermott. Butler had 16 points to help Chicago win its second straight.
Taj Gibson finished with 18 points and eight rebounds for the Bulls.
Mike Conley led Memphis with 28 points and eight assists, and Marc Gasol had 24 points and 11 rebounds.
Chicago was without second-leading scorer Dwyane Wade, who did not play on the second night of a back-to-back after the Bulls beat New Orleans at home Saturday.
The game featured 16 lead changes and 11 ties, with neither team holding a double-digit lead.
