The victory extended Northern Illinois' streak to 17 consecutive road wins, dating to 2012.
The Huskies (3-0) held a 23-point lead in the third quarter before UNLV (1-2) scored three touchdowns and eventually tied the game 34-34 on a 9-yard scoring run by Shaquille Murray-Lawrence and a two-point conversion in the fourth period.
Hare completed 18 of 28 passes for 285 yards and three touchdowns as the Huskies finished with 616 total yards. Hare also ran for 74 yards and a touchdown.
Northern Illinois rushed for 331 yards, with Cameron Stingily leading a group of nine rushers with 102 yards on 17 carries and two touchdowns.
Decker led the Rebels with 397 yards passing, completing 24 of 42 passes for two touchdowns. UNLV had 499 yards of total offense.
The Rebels almost pulled off a comeback after scoring three times in the third quarter. A roughing-the-punter call on Northern Illinois gave UNLV new life when the Rebels were deep in their own territory, and they converted it into a 53-yard scoring pass from Decker to Devante Davis.
Davis finished with six catches for 150 yards and two touchdowns.
Rebels defensive end Jordan Sparkman recovered a fumble by Hare at the Northern Illiniois 10-yard line, leading to a 2-yard touchdown run by Murray-Lawrence that pulled the Rebels to within five points, 31-26.
But the closest UNLV could get was the tie game.
Northern Illinois appeared to take control of the game in the first half, scoring three times for a 21-5 lead and totaling 271 yards in total offense.
After UNLV scored first on a 25-yard field goal by Jonathan Leiva, Northern Illinois grabbed the lead with a 15-play, 76-yard drive that ended with Stingily scoring from five yards out with 7 minute 26 seconds left in the opening quarter.
UNLV cut its deficit to 7-5 late in the first quarter on a safety, but the Huskies ground out two 80-yard scoring drives in the second period to pull away.
Hare, who came off the bench the previous week to lead a 23-15 win over Northwestern, threw TD passes of 12 yards to Keith Harris and 10 yards to Juwa Brescacin.