Auburn (5-1) went on an 8-2 run to start the second half, increasing a one-point halftime advantage into a 29-22 lead on two Ward free throws with 15:55 to go.
After South Florida (6-5) cut the lead back to two, 31-29, the Tigers went on a 14-3 run, culminating with a Denson teardrop in the lane, for a 45-32 advantage with 6:48 to go.
Ward and Sullivan, who both started the Tigers' first five games, came off the bench at the first timeout a little more than two minutes into the game. Tigers coach Tony Barbee said the two came off the bench because they've been nursing injuries and did not practice this week.
The Tigers, who entered Wednesday night in a tie for 337th out of 344 Division I teams with a 57.3 percent free-throw mark, made 15 of 18 (83.3 percent) from the line on the night.
Augustus Gilchrist led South Florida with 10 points, as South Florida struggled to a 33.3-percent night from the field (14 of 42), 22.2 percent from 3-point range (4 of 18) and 50 percent from the free-throw line (8 of 16).
South Florida's 40 points were the lowest for an opponent against Auburn since Alabama A&M scored 40 on Dec. 29, 2008.
South Florida jumped out to a 9-2 lead with 16:49 to go in the first half, thanks in large part to six points from Gilchrist, who hit two jumpers and added a put-back slam dunk.
Auburn missed its first five shots of the game before a breakaway dunk by Chris Denson off a steal stopped the skid with 15:05 left.
The Bulls' lead stayed between one and five points until a Sullivan layup with 31 seconds left in the first half gave the Tigers their first lead of the game at 21-20, an advantage they'd take into halftime.
Both teams struggled to get anything going offensively in the first half. South Florida shot only 39.1 percent (9 of 23) from the field and committed seven turnovers, while Auburn shot 36.4 percent (8 of 22) and turned the ball over eight times.
Gilchrist led all scorers with 10 points in the first half for the Bulls. The senior shot 5 of 7 from the field, leaving the rest of his team to shoot 25 percent (4 of 16).
Ward scored seven in the first half for the Tigers, and Denson added six.