Cherry had NC State's first three touchdowns to help the Wolfpack (3-0) take a 35-7 halftime lead. Brissett threw both of his touchdown passes during an opening half in which the Wolfpack outgained South Florida 343-94.
Cherry entered the game with two career touchdowns - a pair of touchdown receptions in NC State's season-opening 24-23 win over Georgia Southern.
Brissett went 20 for 29 for 266 yards. The Wolfpack finished with 589 yards, compared to South Florida's 159.
Lamar Robbins scored on an interception return for South Florida (1-2).
NC State had allowed combined 57 points in victories earlier this season to Georgia Southern and Old Dominion.
Cherry put South Carolina ahead 14-7 late in the first on a 17-yard reception from Brissett. The Wolfpack took a 21-7 lead 44 seconds into the second when Cherry got his third touchdown of the game with a 3-yard run.
After Cherry opened the scoring with a 17-yard run on North Carolina State's first possession, South Florida tied it at 7 when Mike White threw a career-long 75-yard touchdown pass to Ryeshene Bronson on the first play of the ensuing possession.
White started one week after fracturing his left arm on the Bulls' first offensive play in a 24-17 loss to Maryland. The sophomore, who wore a brace on his injured non-throwing arm, completed 4 of 16 passes for 82 yards.
South Florida's Chris Dunkley returned a punt for a touchdown midway through the first quarter that was negated by a holding penalty.