GLENDALE, Ariz. -- Ezekiel Elliott punctuated his final college game with a record-tying four touchdowns in the Fiesta Bowl, adding another chapter to Ohio State's rich running back tradition.

Elliott rushed for 149 yards and a career-high four touchdowns in the No. 7 Buckeyes' 44-28 victory over No. 8 Notre Dame on Friday at University of Phoenix Stadium.

"All I can say is I'm honored to be a part of this history," Elliott said. "I'm honored to continue the running back pedigree at Ohio State. I'm honored to be thought of as one of the best running backs to come through.

"You think about the great running backs who came through here -- Archie Griffin, Eddie George, Beanie Wells. To be mentioned with those names is a dream come true."

Elliott, a junior, scored on 2-, 1- and 1-yard runs in the first half, and his 47-yard dash on a counter play gave the Buckeyes (12-1) a 35-21 lead with 6:37 left in the third quarter. He has declared for the NFL Draft.

The Buckeyes looked very much like a team that could repeat as the national champion but for a 17-14 walkoff loss to Michigan State on Nov. 21 that snapped their 10-game winning streak and kept them out of the Final Four.

Quarterback J.T. Barrett passed for 211 yards and a touchdown with an interception and rushed for 96 yards as Ohio State opened a 28-7 lead in the second quarter, the largest deficit Notre Dame faced this season.

"I always feel feel like we are one of the top teams in the country," said Barrett, named the offensive player of the game.

"But like I said after Michigan State, that was something that we could have controlled. Losing kind of put our destiny in somebody else's hands. With that, we live and we learn."

Quarterback DeShone Kizer passed for 284 yards and two touchdowns with an interception and rushed for a score as Notre Dame (10-3) suffered its second straight loss. The Irish's other losses were to Clemson and Stanford, both by two points.

Notre Dame wide receiver Will Fuller had six catches for 113 yards and a touchdown, and his 81-yard score brought the Irish within 10 at 38-28 with 11:27 remaining. Running back Josh Adams rushed for 78 yards and a touchdown while starting in place of C.J. Prosise, out with an ankle injury.

Ohio State had a 496-405 yardage edge in total offense.

"Schematically, they do a great job of creating challenging situations with changing numbers and unique plays," Notre Dame linebacker Joe Schmidt said.

"You combine that with Ezekiel Elliott and J.T. Barnett's ability to run the football, and their offensive line doing a great job all day. Their back (Elliott) is very talented, but they did a great job of scheming."

Sean Nuremberger kicked three fourth-quarter field goals for the Buckeyes, his last with 2:42 remaining.

Ohio State scored on its first two possessions with drives of 80 and 43 yards for a 14-0 lead less than halfway through the first quarter.

Elliott scored his first touchdown on a 2-yard run, and after a Notre Dame three-and-out, Barrett completed a 15-yard touchdown pass to wide receiver Michael Thomas with 7:41 left in the quarter.

Notre Dame, shut out in the first quarter for the first time this season, scored on Adams' 3-yard touchdown run halfway through the second quarter.

Elliott scored on 1-yard runs on the Buckeyes' next two possessions for a 28-7 lead.

Kizer scored on a 1-yard keeper with 29 seconds left in the half to make it 28-14. Kizer has 10 rushing touchdowns this season, a school record for a quarterback.

Kizer's 4-yard touchdown pass to wide receiver Chris Brown after Barnett's lone interception made it 28-21, but Elliott scored seven plays later to answer.

"He's a physical back," Notre Dame defensive lineman Sheldon Day said. "He makes his presence known. He did some special things with his feet today."

NOTES: Notre Dame LB and Butkus Award winner junior Jaylon Smith left the game in the first quarter with a "significant knee injury," Notre Dame coach Brian Kelly said. Smith, the Irish's leading tackler with 113, is ranked No. 9 overall by NFLDraftScout.com if he declares for the draft. He had an inflatable cast on his left leg and was on crutches after the game. ... Ohio State DE Joey Bosa was ejected with 5:25 remaining in the first quarter for targeting a Notre Dame player after an interception by Buckeyes S Tyvis Powell. The penalty negated the interception. ... Bosa, RB Ezekiel Elliot and QB Cardale Jones have declared for the NFL Draft, coach Urban Meyer said Thursday. Bosa is projected as the No. 1 pick by NFLDraftScout.com. ... Despite their geographical proximity, the teams have played only five times previously, the most recent being Ohio State's 34-20 victory in the 2006 Fiesta Bowl when Buckeyes quarterback Troy Smith threw for 342 yards and two touchdowns. ... The teams have won 19 consensus national titles, 11 by Notre Dame, and have appeared in 80 bowl games, 45 by Ohio State.