Paul swiped the ball from Ralph Sampson III for the dunk that gave the Illini (12-2, 1-0 Big Ten) a three-point cushion at 73-70. Leonard's layup with 1:11 left made it 78-72 and finished the Golden Gophers (12-2, 0-1).
Paul finished with 21 points. Leonard had 20 and a game-high 11 rebounds for his third straight double-double.
Sampson led Minnesota with a game-high 22 points plus nine rebounds. Julian Welch added 15 points.
The Illini led by 13 midway through the second half before the Gophers stormed back to tie it with just over 6 minutes to play on a 3-pointer by Welch. A pair of Leonard free throws with 7 seconds left sent the game to overtime.