LOS ANGELES (AP) -- Mario Chalmers saved his best for the end.
After scoring just three points in the first half, Chalmers had 17 in the second, including a long 3-pointer and free throw in the final 20 seconds to help No. 4 Kansas outlast Southern California (No. 24 ESPN/USA Today, No. 22 AP) 59-55 Sunday.
"I've always felt like I should get the ball at the end of the game because I feel like I can make a play," said Chalmers, who hit a 3-pointer from about 26 feet to give Kansas (7-0) a five-point lead with 20 seconds remaining.
"The original plan was to get the ball into the post, but they kind of sagged back and I saw there were only five seconds left [on the shot clock]. I got the ball back and just shot it and I was fortunate for it to go."
He hit his 3 after USC had pulled within 55-53 on Davon Jefferson's two free throws with 54 seconds left. Chalmers added a free throw with 3 seconds remaining to cap the scoring.
"They ought to give Chalmers four points from where that shot came from," USC coach Tim Floyd said. "The kid made a big shot."
Freshman O.J. Mayo led the Trojans with 19 points, but was just 6-of-21 from the floor. Jefferson, also a freshman, added 17 points.
"Obviously, he's a great player," Chalmers said of Mayo. "I think we kind of wore him out today."
Chalmers downplayed his heroics at the end.
"It wasn't nerve-racking at all," he said. "We knew they were going to make a little run. We just had to keep our composure and try to finish real strong."
The game was the Jayhawks' first on the road this season and ended a six-game winning streak by the Trojans (6-2).
Kansas coach Bill Self thought the Jayhawks were relatively ragged.
"We never had the game totally under control," he said. "We turned the ball over too much, especially at the end of the game. That should never happen.
"Mario did not play that well overall. He made some deep plays down the stretch, which we needed. It was one of those grind-it-out games. We did not execute very well."
But the Jayhawks got it done, Floyd pointed out.
"They showed their experience and poise when they needed to and we did not," he said. "We played frustrated and took quick shots. It's the way it is with youth. I applaud Kansas.
"I hope we get to that point at the end of the year."
Chalmers had seven rebounds, Darrell Arthur had 10 points and eight rebounds before fouling out late in the game, and Darnell Jackson had nine points and 13 rebounds to help the Jayhawks control the inside for much of the game. They finished with a 42-30 edge on the boards.
Beginning with 9:53 left in the game, the Trojans went a span of more than four minutes without a point. The Jayhawks pulled away by scoring nine points in a row to open a 51-42 lead on a pair of Brandon Rush free throws with 6:39 remaining. Kansas never trailed again.
After the Jayhawks' Russell Robinson hit a 3 to tie it with 8 seconds left in the first half, Jefferson answered with a buzzer-beating jumper to send the Trojans to the locker room with a 27-25 lead.
The Jayhawks were stone cold for the first nine minutes of the game, making just three of their first 14 shots and falling behind 16-6. They began to find the range after that and evened it at 16-16 on Stewart's layup with 5:48 left in the half.
Kansas senior Rodrick Stewart, who had transferred from USC during the 2004-05 season, had four points and seven rebounds against his former team.
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