Flowers and Pelham headlined a physical Golden Eagles front court, which outscored the Pirates 42-20 in the paint and won the rebounding battle 34-21.
Buchi Awaji and Sai'Quon Stone chipped in 10 points apiece for the Golden Eagles (11-8, 1-4 Conference USA), who won their first regular-season conference game since Feb. 17 when they defeated East Carolina 69-59.
Southern Miss shot 48 percent (26 of 54) from the floor in the win, which snapped a two-game losing skid.
Jamar Abrams led East Carolina (6-13, 0-5) with 18 points. The Pirates extended their losing streak to five games, and increased their Conference USA losing streak to 11 games. East Carolina has not won a league game since Feb. 15.