Frazier led his team to consecutive national championships in 1994 and 1995, and is one of six quarterbacks to have done so since the 1950s: Oklahoma's Steve Davis, Nebraska's Jerry Tagge, USC's Matt Leinart, Alabama's A. J. McCarron and Georgia's Stetson Bennett being the others.

He was one of six Nebraska Cornhuskers on this 85 man roster, along with Johnny Rodgers, Rich Glover, Dave Rimington, Dean Steinkuhler and Aaron Taylor.

Frazier was not drafted by the NFL due to a blood clot in his left leg, a side effect of Crohn's disease.

After several years in which the Cornhuskers had suffered blowout losses in bowl games,[14] frequently in Orange Bowl matchups against the University of Miami Hurricanes and the Florida State Seminoles, head coach Tom Osborne changed his recruiting strategy in the early 1990s and began to recruit faster players at all positions.

3 college recruit in the country by analyst Tom Lemming,[17] led Nebraska to four consecutive New Year's Day bowl games.

[18] Frazier joined the Nebraska football team as an 18-year-old true freshman in the summer of 1992, at 6–1 and 190 pounds, and began as a backup to senior Mike Grant.

He played well in the FedEx Orange Bowl on January 1, 1993, against an 11–1 Florida State team led by quarterback Charlie Ward, wide receiver Tamarick Vanover, and linebacker Marvin Jones.

[39] Dropback passer Brook Berringer led the team back to the FedEx Orange Bowl with a 12–0 record, where the Cornhuskers faced the third-ranked Miami Hurricanes in the de facto national championship game.

[40] Frazier started the game, but was replaced by Berringer after a deep throw to the end zone on Nebraska's initial drive resulted in a turnover.

[49] The 1995 roster matched Frazier with a number of running backs that included Lawrence Phillips, Ahman Green, Clinton Childs, Damon Benning, Joel Makovicka, and Jay Sims, to form a backfield that set an NCAA record 7.0 yards per rushing attempt.

[54] Frazier collected his third consecutive national championship game MVP award as the Cornhuskers defeated Florida's "Fun 'n' Gun" offense by a score of 62–24.

[57] On what appeared to be a routine short-yardage option sweep to the right sideline in the closing seconds of the 3rd quarter, Frazier kept the ball, turned upfield, and broke seven tackles in a career-high 75-yard touchdown run that was named by Sports Illustrated as one of college football's greatest plays.

[58][59] CBS reporter Michele Tafoya handed Fraizer the microphone during the postgame celebration following the game: "Oh listen, I had a great career at Nebraska…There is no better way to end it; I want to thank all the fans for all the support, and I want to thank all my teammates—most of all important, I want to thank the Lord Jesus Christ above, because without him, I wouldn't have been able to accomplish anything I have.

[61] Frazier's place in the University of Nebraska's football history was firmly secured after helping the Cornhuskers win multiple national and conference championships, going 45–4 with 5,476 total yards of offense and 79 touchdowns.

[64] Sports Illustrated's Tim Layden, who covered Frazier in the Tostitos Fiesta Bowl, discussed his leadership and toughness following Nebraska's 62–24 dismantling of the Florida Gators.

"On that memorable 75-yard touchdown run, Frazier broke seven tackles and dragged two Florida defenders several yards before shaking free and rolling down the sideline alone," Layden elaborated.

"And after playing brilliantly in both Nebraska's 18–16 Orange Bowl loss to Florida State in 1994 and the Cornhuskers' 24–17 national-title victory over Miami last season, he must now be considered one of the best big-game quarterbacks in college football history—its Joe Montana.

[67] Frazier won the MVP award for his 34–18 victory in the East-West Shrine Game, nationally televised on ESPN on January 13, 1996.

[70] Recruiting analyst Forrest Davis' publication had listed Frazier's speed in the 40-yard dash as 4.50 seconds when he came out of high school,[71] and his test results at Nebraska had been similar.

[72] Due primarily to health issues, Frazier went unselected in the NFL Draft, but received an offer from the Montreal Alouettes of the Canadian Football League.

He signed a contract with the Alouettes on July 15, 1996, and served as the third-string quarterback behind starter Tracy Ham and top reserve Jim Kemp.

Frazier played in only one game, on August 30, 1996, a 17–6 loss to the Ottawa Rough Riders in which he came off the bench in the 4th quarter and completed 6 of 17 passes for 55 yards.