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Navy (6-1, 4-0 American Athletic Conference) never led until Reynolds bulled in from the 1 to make it 22-17 with 6:58 left. After South Florida (4-4, 2-2) fumbled the ensuing kickoff, Reynolds clinched it with another 1-yard touchdown run with 1:49 remaining.
Reynolds, a senior quarterback, has 77 career rushing TDs, tied with former Wisconsin running back Montee Ball (2009-12) for most in NCAA history.
Reynolds finished with 117 yards rushing, Dishan Romine had 115 and Chris Swain totaled 131 for Navy.
The victory made the Midshipmen bowl eligible for the 12th time in 13 years.