Iowa, which rallied from a 16-point deficit in the second half, made 29 of 33 free throws. Indiana made only 19 of 34 and missed six in a row.
Trailing by one point with eight seconds to play in overtime, Iowa's Acie Earl missed one shot and Chris Street missed another on the rebound before Moses' winning tip.
"I didn't see the clock until I tipped the ball and it went in," said Moses, of Mission Hills Alemany and Gardena Serra high schools. "Then I was like, 'Hey, it's good. They can't take this from us.' "
Indiana is 22-4 and 10-3 in the Big Ten Conference. The Hawkeyes are 18-8 and 7-7.
The Utes (25-2, 14-1) led, 56-53, when Colorado State's Tracy Jordan missed two free throws with about four minutes left. Utah scored the next six points.
Grant, who had 19 points, made five free throws to put the game away for the WAC champions.
Temple, playing without guard Mark Macon for the first time in 120 games, got 20 points from Donald Hodge and beat Massachusetts, 80-70, in an Atlantic 10 Conference game at Amherst, Mass. Macon sprained his right ankle earlier in the week and is expected to miss one more game.
Michael Talley scored Michigan's final six points to lift the Wolverines past Wisconsin, 65-62, in a Big Ten Conference game at Ann Arbor, Mich. . . . Tank Collins, from Pomona High, scored 24 points and grabbed nine rebounds to lead New Orleans over Central Florida, 77-65, at Orlando, Fla.
Troy Bowe scored seven of his 24 points in overtime to lift Hawaii past San Diego State, 84-79, in a Western Athletic Conference game at San Diego. . . . Kevin Weatherby scored a career-high 27 points as St. Mary's beat Portland, 100-90, in a West Coast Conference game at Portland, Ore. . . .Jarrod Davis scored 34 points and grabbed 10 rebounds to lead Gonzaga to a 95-72 WCC victory over the University of San Francisco at Spokane, Wash. Orlando Smart led the Dons with 26 points.