Collins had eight consecutive points, including two layups, to put the Bulls ahead 70-62 with 4 1/2 minutes to play. The point guard's in-close basket made it 75-64 2 minutes later.
South Florida (11-17, 2-14 Big East) also got 13 points from Martino Brock.
The teams are tied for last place in the Big East.
The Blue Demons had a 9-0 run, keyed by Charles McKinney's three-point play, to pull even at 56 midway through the second. DePaul took its first lead, 60-58, when Jamee Crockett made two free throws with 8:13 left.
Fitzpatrick connected on three 3-pointers during a 12-4 stretch that gave South Florida a 53-45 lead with 13 minutes to play.
DePaul, which trailed by 11 in the first half, tied it at 37 on Donnavan Kirk's basket 1 minute into the second half.
Rudd had 10 points as South Florida grabbed a 37-33 halftime lead.
The teams started the game by missing 11 combined shots and turning the ball over three times.
Rudd made the first basket of the game, a 3-pointer, with 16:14 left in the opening half. Young got the Blue Demons on the board with a layup on the ensuing possession.
South Florida took a 14-6 advantage on Fitzpatrick's long-range jumper 8 minutes into the game.
After DePaul got within 23-20, South Florida went on a 10-2 run for a 33-22 lead. Rudd ended the surge with his trey with 6 minutes remaining.
A 3 by Crockett cut the DePaul deficit to 35-33.
South Florida has won the last eight games between the teams.
Malik Newman, who had widely been considered a one-and-done player, has chosen to transfer to Kansas to continue his college career.
Avery Johnson's first season as a college coach was a success by most measures, and he'll aim to keep the Crimson Tide rolling in the right direction.
Gonzaga has signed California transfer Jordan Mathews to a financial aid agreement for the 2016-17 season.