A jumper by LaTre'e Russell gave Norfolk State (2-2) a 9-7 lead and the Spartans never trailed again.
The Tigers would get no closer than nine the rest of the way.
Jamel Fuentes tied a career-high with 11 assists, including four during the decisive run.
Chris Thomas scored a career-high 28 for Texas Southern.
RaShid Gaston had 14 points for Norfolk State.