Texas Tech's bench kept coach Chris Beard's team alive against Virginia, but just couldn't overcome a deficit in overtime.
Brandone Francis had 15 points and Kyler Edwards had 10, helping to make up for off games from star guard Jarrett Culver and forward Tariq Owens.
Owens, who was trying to play through a sprained ankle, has fouled out. He finished with just three points and five rebounds.
A Texas Tech victory against Virginia in the NCAA Tournament championship game would have marked an odd first: The Red Raiders would become the first team to win the title after losing their first conference tournament game.
The Red Raiders were the No. 1 seed in the Big 12 Tournament and were bounced by last-place West Virginia on March 13 in what was probably the most surprising result from the major conference tournaments.
If the fortunes had been reversed, Texas Tech would have become the first team since Connecticut in 1999 to win a title the same year it makes its first Final Four.
UConn had reached the Elite Eight three times in the previous nine tournaments, and had three other Sweet 16 appearances before winning it all in 1999 by beating Duke. The Red Raiders had never been to an Elite Eight before last season and had only three Sweet 16 appearances in the previous 40 years. From 2008-15, Tech didn't even make the NCAA Tournament.
Texas Tech defeats Michigan State, advances to National Championship
Texas Tech fans tear gassed while celebrating their win against Michigan State