Providence (13-11, 5-7), which has won three consecutive Big East games for the first time since 2008-09, also got 13 points from Bryce Cotton. The Friars were coming off a 54-50 win over then-No. 17 Cincinnati on Feb. 6 in which Batts had 25 points and nine rebounds.
Batts scored 16 of his points during the second half. Providence, keyed by Vincent Council's 3-pointer and a go-ahead basket by Kris Dunn, scored the first 17 points of the second to take a 42-36 lead with 13 minutes left.
Rudd made a 3-pointer as the Bulls pulled within 66-61 with 2 minutes to go.
Council, who finished with 11 points, and Cotton helped preserve the Friars' win by making a combined six free throws down the stretch.
JaVontae Hawkins scored South Florida's first points in the second half on a basket with 12:57 remaining.
Providence went ahead 48-38 on Henton's dunk, which was part of a 23-2 second-half opening surge.
Rudd had 12 points to help South Florida grab a 36-25 halftime lead. The forward returned after missing one game because of a groin injury.
Anthony Collins' layup gave South Florida a 34-20 advantage 2 minutes before intermission.
Fitzpatrick made a 3 and Rudd had a dunk as South Florida took an early 10-2 lead. Baskets by Kore White and Collins extended the Bulls advantage to 20-7.
Henton connected on a long-range jumper during a 10-0 run that got Providence within 20-17 midway through the first.
The Bulls ended a 6-minute scoring drought when Martino Brock's jumper made it 22-17 with 6:30 to go in the half.