When did Texas last lose a football game to an unranked opponent?

It's looking like Texas is going to lose to unranked UCLA - when was the last time they lost to an undefeated opponent? Colt McCoy lost a game in his first season, but it was to Ohio State, but I ume they were ranked. The previous season, Texas was undefeated, and in 2004 they only lost to Oklahoma, which could very well have been ranked at the time. I'm wondering when the last time they got beat by a team that wasn't ranked?