Hofstra led 33-31 at the half before Drexel used a 16-12 run to move ahead 47-45 with 10:36 left.
Agudio made back-to-back layups to give Hofstra a 49-47 edge, but Rodgers tied the score with a layup.
Jenkins then took over, scoring six straight points with four free throws and a driving layup to put Hofstra ahead for good at 55-49.
Drexel closed within four points twice down the stretch, but Johnson countered with a jumper and 3-for-4 shooting from the line to seal the win.
Hofstra shot 26-for-51 (51 percent), while Drexel went 21-for-55 (38 percent). The Pride outrebounded the Dragons 37-30.