The Jayhawks improved to 7-0 on the season, while USC dropped its second contest of the year for a 6-2 overall record.
Sophomore Darrell Arthur was the only other Jayhawk in double-figures with 10 points. The 6-9 forward also went up for eight rebounds in the contest.
Senior forward Darnell Jackson paced KU on the boards pulling down a career-high 13 rebounds for the game to compliment his nine points.
Kansas opened the contest with the first four points but went scoreless over the next five minutes as USC went on an 11-0 run. KU faced its biggest deficit of the season down 16-6 just under 10 minutes into the first half.
KU responded with a 10-0 run to tie the score at 16-16 with 5:47 left to play in the opening half. As the first 20 minutes wound down, USC converted on a three-point play for a 25-20 advantage with 51 seconds to go.
A bucket by senior Rodrick Stewart followed by a three-pointer from senior Russell Robinson locked the score at 25 with just eight seconds remaining, but USC hurried down the floor and took a two point lead into the locker room with a shot at the buzzer, Kansas' first halftime deficit of the season.
The teams went back and forth with four ties and five lead changes in the first 10 minutes of the second half.
The Jayhawks took a nine-point lead with 6:29 remaining in the game, its largest lead of the game on a pair of junior Brandon Rush free throws.
With 1:50 remaining USC to cut its deficit to four as KU led 55-51. The Trojans then made two free throws to come within two with just under a minute to play.
With the shot clock under five, Chalmers drained a long three-pointer to give the Jayhawks a five-point cushion with 18 seconds on the clock. He then sealed the game with a free throw to give Kansas a 59-55 victory.
The Jayhawks return home Wednesday, Dec. 5 against Eastern Washington. Tip off is scheduled for 7 p.m. from Allen Fieldhouse.