Reynolds scored on runs of 47 yards, 11 yards and 1 yard. The sophomore has 29 rushing touchdowns, breaking the single-season mark for a quarterback previously held by Ricky Dobbs (Navy, 2009) and Collin Klein (Kansas State, 2011), both of whom had 27.
"Coming into the game, I wasn't too concerned about the record. If I broke it, I broke it. If not, oh well," Reynolds said. "My main concern was trying to get the W. If that involved me getting zero touchdowns and everyone else having a field day, I was good with that."
It didn't work that way at all. Reynolds ran 30 times on a frozen, snow-covered field. He also caught a 2-point conversion pass on a trick play following his second touchdown.
His third score with 46 seconds left in a lopsided game gave him 176 points for the season, breaking the school record of 174 set by Bill Ingram in 1917.
"The thought did come across my mind to take a knee," Niumatalolo said. "But then my thoughts went to, I have a kid that has a chance to break a record that's hard to come by."
Navy (8-4) won the Commander-In-Chief's Trophy for the second consecutive season and ninth time in 11 years. The trophy is awarded to the service academy with the most victories in games between Navy, Army and Air Force.
The Midshipmen haven't lost to Army since 2001 and lead the series 58-49-7. Navy's 12-game run is the longest in the history of the rivalry that began in 1890.
Niumatalolo became the second coach in Navy history to start his coaching career 6-0 against Army, matching Paul Johnson (2002-07).
The Midshipmen will conclude their season in the Armed Forces Bowl against Middle Tennessee State on Dec. 30.
Army (3-9) fumbled five times and was intercepted once in its fifth straight defeat.
Embattled coach Rich Ellerson fell to 0-5 against the Midshipmen and 20-41 overall since taking the job in December 2008.
"You turn the ball over against a good football team, you give up big plays on defense, you take some big hits in the penalty game against a good football team, don't be surprised if the score gets upside down," Ellerson said.