Brandon Monroe also grabbed 11 rebounds for the Spartans (6-11, 4-2 Mid-Eastern Athletic Conference), who have strung together three straight wins for the first time this season. O'Quinn was also 4-for-6 from beyond the arc.
The Bulldogs have lost four straight MEAC games.
South Carolina State led 32-21 midway through the opening half and maintained a two-point halftime lead over Norfolk State. But the Spartans outscored the Bulldogs 33-25 in the second half to seal the win.
South Carolina State committed 26 turnovers in the game.