The sophomore quarterback also rushed for a 7-yard score as the Golden Flashes (1-6) snapped a six-game losing streak, winning for the first time since last Nov. 19 at Ohio.
Reardon connected with tight end Casey Pierce on a 10-yard score in the second quarter to put the Golden Flashes ahead for good at 13-10. They later teamed up for a 5-yard TD.
Reardon, who finished 27-of-40 with an interception, also tossed an 8-yard TD to wide receiver Chris Humphrey.
The Black Knights (2-5) amassed 295 yards on the ground, but senior Angel Santiago only completed 3-of-10 passes for 17 yards and an interception on the rainy, 46-degree afternoon.
The Black Knights have not won a game at an opponent's stadium since 2010, when they defeated Southern Methodist in the Armed Forces Bowl. Their last regular season road victory occurred at Kent State four years ago.
Anthony Melchiori was perfect on four field goal attempts for the Golden Flashes, who are 0-3 in the MAC East Division.
Kent State, which scheduled the Black Knights for its homecoming game, started eight sophomores and six freshmen.
Daniel Grochowski opened the scoring with a 32-yard field goal for Army just 3:27 into the first. Black Knights cornerback Josh Jenkins picked off Reardon on the opening play of the game at the Kent State 37.
The Flashes answered with a 27-yard field goal by Melchiori, tying the contest after a quarter.
Melchiori added a 29-yarder two minutes into the second, completing a season-long 84-yard drive by the hosts at Dix Stadium.
Maples scored on a 2-yard run, giving Army a 10-6 lead with 7:56 left in the first half.
Kent State's lead was sliced to 20-17 six minutes into the third on an 8-yard run by Giovannelli. The 6-foot-1, 201-pounder set up the score by gaining 37 yards on a pitch from Santiago, taking the ball to the Flashes 29.