Reynolds' three scores gave him 29 for the season, setting the collegiate mark for most rushing touchdowns by a signal-caller in a single season. He broke the old record of 27 held by Navy's Ricky Dobbs (2009) and Kansas State's Collin Klein (2011).
Reynolds finished with 136 rushing yards, including a 47-yard TD run in snowy conditions at Philadelphia, as the Midshipmen (8-4) warmed up for the Armed Services Bowl with a fourth straight win overall.
The Black Knights (3-9), meanwhile, ended the season with a fifth straight loss.
Quarterback Angel Santiago got Army's only TD on a 4-yard scoring run.