The Bobcats won their fourth straight and improved to 6-2 under new coach Paul Silas.
Charlotte trailed by one heading into the fourth period but owned a three-point cushion when Augustin was fouled with 23 seconds left. His two free throws boosted the lead to five and he made two more with 18 seconds left.
A missed 3-point try by Luol Deng with 13 seconds to go sealed Chicago's fate.
Augustin scored 22 points to go with 12 assists and Stephen Jackson added 16 for the Bobcats. Charlotte let a 17-point, second-quarter lead get away before staging a rally of its own.
Carlos Boozer had 23 points and 14 rebounds for the Bulls, who had won their previous two games.
Swim Week Miami Beach 2014 [PHOTOS]