Collins also had seven assists for the Bulls (1-1).
"I just want to tally up some wins and get our team going a little bit," Fitzpatrick said. "Get some confidence."
Maryland-Eastern Shore (0-4) got 14 points from Ronald Spencer. Troy Snyder, who finished with 12 points, got Maryland-Eastern Shore within 36-28 early in the second half.
"We played about as well as we could in spurts, but we didn't sustain anything," Maryland-Eastern Shore coach Frankie Allen said. "They did an outstanding job of really keeping us back on our heels."
Victor Rudd hit a 3-pointer that gave South Florida a 52-32 advantage with 12 minutes to play.
Collins had 11 points to help the Bulls take a 34-23 halftime lead. The guard hit a 3-pointer, and Fitzpatrick scored seven points during a 15-0 run that put South Florida up 15-6 early in the game.
"It was a good win," Bulls coach Stan Heath said. "There are still some things we need to get better at. The team is still just coming along. We're trying to figure some things out."
South Florida scored 15 points off Maryland-Eastern Shore's first-half turnovers.
The Hawks made just 18 of 55 shots (32.7 percent) overall.
"Their overall size just kind of wore us down as the game went on," Allen said.