Longhorns devastate a good Oregon team 71-7. 

Even without a bowl appearance, the 1941 Longhorns are one of the most important teams in Longhorn football history.

They notched the programs' first #1 ranking ever, and two Horns make the consensus All-American team. The Longhorns win the first-ever Golden Hat Trophy against OU. Texas coach Bible is offered an invitation to the Rose Bowl if he will cancel the game Oregon game, but he refuses. That decision cost him possible invitations to three bowl games. The story is told by Stephen Ross in the article below.

The article below is from Texas Longhorn History: The Rose Bowl That Almost Was

By Stephen Ross Dec 7, 2016, 12:12pm CST

β€œOregon State was the best representative for the Rose Bowl, and their AD was an old friend of Bible’s. He pushed hard for Texas to get an invitation. While waiting to hear from the Rose Bowl, Texas turned down invitations to both the Orange Bowl (they took TCU instead) and the Sugar Bowl. 
The Saturday after Thanksgiving, Oregon State edged Oregon 12-7, and that made the Rose Bowl committee nervous. Texas would finish the regular season December 6th by hosting the Ducks. The committee feared that an Oregon win would embarrass the Rose Bowl, so they chose #2 Duke instead of #4 Texas to play in the Rose Bowl. 
Texas was shut out of any bowl, and Oregon would pay for it – to the tune of a 71-7 beating at the hands of the Horns on December 6th. The team was so pissed at the snub that 8 different players scored. Bible said afterward that there was no stemming the tide of anger short of telling his players not to try. 
β€œEvery single one of them was leaning forward, β€œ Bible said. β€œWe put everybody in the game. You put a new boy out there, he’s been waiting for his opportunity, and when he gets in, he goes all out.”
Less than 24 hours later, the Japanese attacked Pearl Harbor. Fear of an expanding war towards the west coast led Rose Bowl officials to think about cancelling the game. After a few days they decided to move the contest to Durham, North Carolina, home of the Blue Devils. Oregon State edged Duke 20-16 in Durham on January 1st 1942.
Two plays. 30 seconds of action. That is what separated Texas from hosting the 1942 Rose Bowl. β€œ