The Golden Eagles (10-6), who snapped a three-game losing streak, shot 50 percent from the field (29 of 58) and made a season-high 10 of 23 from the 3-point arc.
Southern Miss opened with a 10-2 run and led 25-13 before the midway point of the first half.
Cal State Bakersfield (2-14) did not score in the final 3:15 of the first half, allowing the Golden Eagles to jump out to a 40-23 lead at the break. Southern Miss took its biggest lead in the second half, when Johnson made a 3-pointer to extend the advantage to 25.
Cal State Bakersfield closed the game with a 16-6 run.
Stephon Carter scored 25 points to lead the Roadrunners, who never led. They have lost four straight and eight of their past nine games.
Southern Miss had a season-high 22 assists, and a season-best 22-9 assist-to-turnover ratio. The Roadrunners had 12 turnovers, leading to 16 Golden Eagles points.
The contest was the last nonconference game for Southern Miss and one of just two nonconference home games against Division I opponents.