With James suspended for a game, Barner scored five touchdowns, four on the ground and another via a pass from Thomas. He ran for a career-high 147 yards as Oregon racked up a school-record 720 yards in total offense.
Thomas completed 13 of 23 passes for 220 yards and two scores in his debut as starter after the dismissal of Masoli in the offseason.
If the Ducks were trying to put their troubled recent past behind them, it worked.
"I guess it says a lot," Barner said. "Numbers don't lie."
Oregon's point total tied the Autzen Stadium record the Ducks set in 1999 against Nevada. The most points Oregon has ever scored is 115, against Puget Sound back in 1910.
New Mexico was also looking for a fresh start. The Lobos were 1-11 last season under coach Mike Locksley, who had an altercation with a former assistant and was named in a sexual harassment complaint.
But the Lobos, who managed just 107 total yards on offense, were no match for last year's Pac-10 champions. B.R. Holbrook made his debut as New Mexico's starter, and completed just 11 of 24 passes for 70 yards with two interceptions.
"We're disappointed. I feel like our team has a different mentality from last season, but we didn't execute today," Holbrook said. "Oregon is the reigning Pac-10 champ, so you have to give them credit. But you never think things will go that badly."
Barner subbed for James because the running back was suspended for a game after pleading guilty to a misdemeanor harassment charge that stemmed from a conflict with an ex-girlfriend.
Last season James grabbed national attention by rushing for a team-high 1,546 yards, setting a new record for freshmen in the Pac-10. He averaged 6.7 yards and added 14 TDs to earn the league's freshman of the year honors.
James watched from the sideline Saturday wearing an "O" T-shirt and khaki shorts. He will return to the Ducks next weekend when they visit Tennessee.
Also a return specialist, Barner had 1,553 all-purpose yards last season. He had 225 against New Mexico, and his one catch was a 60-yard catch and run from Thomas in the second quarter.
"I've been saying all along, I think he's the most underrated player in the country," Oregon coach Chip Kelly said. "Today he got a chance to shine. We've always felt that we've had 1A and 1B. We run the ball 40 times a game; one guy is not going to get all the carries."
Standing in for Barner on the return team was Cliff Harris, who returned two punts for touchdowns, an Oregon record for one game.
Masoli had been expected to lead the Ducks at QB this season, but he was accused in a fraternity house theft in January and wound up pleading guilty to a burglary charge. Kelly finally kicked him off the team when he was stopped by police for a traffic violation and marijuana was found in the car.
Masoli has since gone to play at Mississippi, which was upset by Jacksonville 49-48 in double overtime Saturday.
Thomas played in five games as a true freshman in 2008, completing 16 of 33 passes for 268 yards and three touchdowns. Called upon when Oregon was hit by a slew of injuries, Thomas came close to leading the Ducks to a come-from-behind victory against Boise State that season before redshirting in 2009.
"I wasn't overconfident because I never knew what was going to happen," Thomas said. "I needed to come out today and have a good game. I took a couple of hits but that's what I wanted to do to get me back into a rhythm."
The Lobos had a setback in the first half when defensive lineman Carmen Messina, who led the nation with 162 tackles last season, got hit hard and injured his left ankle. He did not return.
New Mexico said details about the injury were not known. Messina planned to return to New Mexico for an MRI on Sunday.
New Mexico is now 7-44 against ranked opponents. The last time the Lobos played a Pac-10 opponent, they beat Arizona 36-28 in 2008.
It was the Lobos' biggest margin of defeat since losing 94-17 to Fresno State in 1991. The last time the Lobos were shutout was in 2007, when they lost 37-0 to TCU.
New Mexico hosts Texas Tech next weekend.
"This was a wake-up call for the whole team. We can't point fingers and fall apart," defensive end Johnathan Rainey said. "We need to come together as a team and make up for each other's mistakes."
Revisiting the best Heisman websites of the 2000s
Take an internet trip down memory lane as we share the tales behind some of the most famous Heisman campaigns of the 2000s.
ASU, NCAA sued over death of linebacker found to have CTE
The father of a former Arizona State linebacker has filed a wrongful death lawsuit against the school and NCAA, alleging that his son's suicide happened during a mental breakdown caused by four concussions he suffered while playing football.
NCAA eases rules for bowl eligibility for this season only
The NCAA's Division I Council announced Wednesday it has approved a blanket waiver request for the 2020-21 bowl season that eases rules toward bowl eligibility.
St. Thomas to jump from Division III to Division I
The Tommies, who previously secured a spot in the Summit League for all but three of their 22 varsity teams, will join the Pioneer League for football and the Western Collegiate Hockey Association for women's hockey.
Missouri coach Eli Drinkwitz using 'influence' to push mask wearing
Missouri coach Eli Drinkwitz is encouraging folks to wear masks when they are out in public, which health experts insist is among the best ways to mitigate the spread of the coronavirus, even though it has become a politicized issue.
Wisconsin uniforms to feature black 'W' on crest
After athletes had pushed for the change of the university's crest, the University of Wisconsin will now go with a black "W" on all uniforms in an effort to support Blacks and other under-represented communities.