Beck set the record a year ago with 352 yards in a 35-28 loss to California.
"This is the way we planned to go out," said Beck, who was partly responsible for the MVP award handed out to BYU tight end Jonny Harline. The fellow senior caught nine passes for a career-high 181 yards - also a Las Vegas Bowl record - and a touchdown.
Beck started slowly, mostly because of dropped passes. He misfired on his first four attempts as BYU went scoreless in the first quarter for the first time since last year's bowl game. But two of the passes were on target, only to be dropped by Matt Allen and Curtis Brown.
The drops, however, didn't stop Beck from slinging the ball downfield.
"I know these guys well enough not to count them out," Beck said of his targets. "I didn't tell them anything except to chill. Even though they drop some passes, I'll always have confidence in them."
Beck spread the ball to eight different receivers and connected 12 times on passes to running backs.
Brown caught seven passes for 55 yards - his most receptions since hauling in 11 balls at Boston College on Sept. 16. Manase Tonga caught four passes for 52 yards and a touchdown that capped the scoring in the fourth quarter.
Beck also showed that Oregon counterpart Dennis Dixon wasn't the only fleet-of-foot quarterback on the field Thursday night. Early in the fourth quarter, Beck dropped back, found no one open in the end zone, tucked the ball and sprinted 13 yards to the pylon. It was his sixth touchdown run of the season and his longest run of the year.
"The start wasn't how we would have liked it," BYU coach Bronco Mendenhall said, "but the end was just right."