It was the first loss of the season for CMU (3-1), which led for the vast majority of the game. Austin, a graduate transfer from Vanderbilt playing in his first season at CMU, scored 30 points.
"We got to the point where we had a chance to win the game, but we understand that over a 30-, 32-game season that there's going to be a lot of these (close) games," CMU coach Keno Davis said. "We understand that this is one game, this wasn't to end the season. This just puts us in a tough spot in having a day off (on Saturday) to have to sit on the ending of this game.
"Knowing the character of our team I'm sure we'll respond well in days to come."
The Chippewas close the Junkanoo Jam on Sunday (6 p.m.) against San Jose State.
HOW IT HAPPENED
The Chippewas led, 76-73, after a Kevin McKay layup with 27 seconds left. Weber State (3-1) drew to 76-75 on two Jerrick Harding free throws with 20 seconds to play.
CMU's David DiLeo missed two charity tosses with 9 seconds left. The Wildcats rebounded, got the ball up the court to Barnes, a freshman, who beat the buzzer with the game-winning triple from 25 feet.
TIGHT GAME
The game featured nine ties and 10 lead changes. The Chippewas' largest lead, 10 points, came near the midway point of the first half; the Wildcats' largest lead was three points, which came with under a minute to play in the first half.
LEADERS
Austin, who added six rebounds, was one of four Chippewas to finish in double figures. McKay added 12 points and a team-high seven rebounds, DiLeo made four of his six 3-point attempts to finish with 12 points, and Rob Montgomery added 10 points.
Harding went 11-for-14 from the free throw to finish with 25 points to lead Weber State.
INJURY UPDATE
Both Roundtree and McKay received medical attention in the second half. Roundtree suffered a cut to his face, and McKay was sent to the floor following a collision.
Roundtree was to receive stitches following the game, while McKay "had his teeth knocked out," according to Davis.