South Dakota trailed by 11 points early in the second half, but stormed back to go up by 13 with 3:35 left on Casey Kasperbauer's 3-pointer.
Larson's made free throws with 4 seconds left gave South Dakota a 72-69 lead. Denver turned the ball over on its possession and Dejon Davis sealed it with a layup before the buzzer.
Kasperbauer had 15 points for South Dakota (7-9, 1-1 Summit) and James Hunter added 12.
Byrd converted four free throws, on back-to-back possessions, to give Denver an 11-point lead, its largest of the game, with 16:08 left.