Tagovailoa received the Maxwell Award for player of the year while Murray was named the nation's top quarterback with the Davey O'Brien Award at the College Football Awards show in Atlanta.
Earlier in the day, the Walter Camp Award for best player went to Tagovailoa, while Murray won the Associated Press' Player of the Year. They are both finalists for the Heisman, along with Ohio State quarterback Dwayne Haskins.
Will college football's most famous trophy go to Tagovailoa? The past four Maxwell winners and past five Walter Camp winners have all gone on to win the Heisman.
Or will the Heisman go to Murray? This is the sixth time in the past 15 seasons that different quarterbacks took home the Maxwell and Davey O'Brien awards, and in four of the previous five times, the Heisman went to the O'Brien winner. And only five Heisman winners have failed to win AP Player of the Year since the award started in 1998.
Tagovailoa, a sophomore, has thrown 37 touchdown passes to just four interceptions while leading the undefeated Crimson Tide to the top spot in the College Football Playoff rankings. He is the third Alabama player to win the Maxwell after AJ McCarron in 2013 and Derrick Henry in 2015.
Murray, a junior who plans to focus on baseball in the future, had a 96.0 quarterback rating, the highest in the Football Bowl Subdivision in at least the past 15 years, and was responsible for 51 touchdowns, tied with Haskins for the most in FBS. He is on pace to become the first FBS starting quarterback to average at least 300 passing yards and 60 rushing yards per game.
Murray's Davey O'Brien marked the fifth time an Oklahoma QB claimed the honor, after Baker Mayfield, who won last season, Sam Bradford in 2008, and Jason White in both 2003 and 2004. Running back Billy Sims also won the award in 1978 before it became quarterback-exclusive in 1981. The five different players broke a tie with BYU for the most by any school.
Murray wins Davey O'Brien best QB award
Oklahoma's Kyler Murray edges Tua Tagovailoa and Gardner Minshew II for the Davey O'Brien award for best quarterback.
Among the other awards given out in Atlanta on Thursday night:
Bednarik Award: Josh Allen was named defensive player of the year; he's the first Kentucky player so honored, but this is the sixth consecutive season the award went to an SEC athlete. Allen led the conference with 14 sacks from his linebacker spot, bringing his career total to a school record 28.5.
The award comes after Allen also won the Bronko Nagurski Trophy as top defensive player on Tuesday.
Doak Walker Award: Jonathan Taylor became the fourth Wisconsin player to be named the nation's top running back after Ron Dayne in 1999, Montee Ball in 2012 and Melvin Gordon in 2014. He leads the FBS with 1,989 yards and has rushed for 100 yards in 11 of 12 games this season.
Fred Biletnikoff Award: Jerry Jeudy was honored as the top wide receiver, joining Amari Cooper as the only Alabama players to win the award. Jeudy, who had 1,103 receiving yards this season, led the SEC with 12 touchdown catches.
Jim Thorpe Award: Georgia's Deandre Baker received the award for outstanding defensive back. Named to the All-SEC first team by both the AP and coaches, he had two interceptions and nine passes broken up.
Outland Trophy: Alabama defensive tackle Quinnen Williams was named the best interior lineman after racking up eight sacks and 18 tackles for loss.
Ray Guy Award: The award for the nation's top punter went to Texas A&M's Braden Mann, who led the FBS with an average of 51.2 yards per punt.
Lou Groza Award: Syracuse's Andre Szmyt was named the top place-kicker after leading the FBS with 28 field goals, three more than any other player, and setting a school record with 141 points. He is the first Syracuse player to win the award, and the first from the ACC since Florida State's Roberto Aguayo in 2013.
Earlier this week, the Butkus Award for top linebacker went to LSU's Devin White. Iowa's T.J. Hockenson became the first sophomore to win the John Mackey Award as the nation's top tight end, while NC State senior Garrett Bradbury took home the Rimington Trophy as the top center.
The honor of the best holder, the Peter Mortell Award, went to the outspoken Mac Loudermilk of UCF, who also serves as the unbeaten Knights' punter, and called himself "an all-around athlete, really," in accepting the award via a taped video that aired at Thursday's award show.
On Wednesday, Notre Dame's Brian Kelly became the first to win the Home Depot Coach of the Year Award for a third time, and Alabama offensive coordinator Mike Locksley, who has accepted the head coaching position at Maryland, won the Broyles Award as the top assistant Tuesday.
The William V. Campbell Trophy, known informally as the "Academic Heisman," went to Clemson defensive tackle Christian Wilkins, who will graduate with a master's degree in athletic leadership this month. Notre Dame linebacker Drue Tranquill won the Wuerffel Trophy for community service.