Victor Rudd had 10 points for the Bulls (2-1), who beat Maryland-Eastern Shore 78-59 on Friday night.
"We played well," South Florida coach Stan Heath said. "We're steadily getting better and better. I know we've got a ways to go, but the energy and the intensity on the defensive end was very strong."
"I liked our character," Loyola coach Porter Moser said. "We want to be good, and we're going to be good. We have to learn from every game."
Rudd hit a 3 and Collins made a free throw to extend the Bulls' lead to 47-28 with 13:30 to play.
White had 10 points as South Florida grabbed a 38-21 halftime lead. Collins' three-point play put South Florida up 22-14 with six minutes left. White had a slam and layup to make it 36-19 late in the half.
"Collins is really good," Moser said. "He plays a great floor game. He's one of the most patient guards with the ball that I've seen off ball screens in a long time."
Collins also had six assists.
Both teams made just 1 of 6 shots over The Opening four minutes of play. Averkamp, who hurt his right ankle in Friday's 81-71 loss to Western Michigan, got the first basket with 16:53 left.
Loyola has not beaten a Big East Conference team since a 70-58 victory over Notre Dame on Jan. 24, 1994.