MINNEAPOLIS — A year after exiting the court as a picture of embarrassment, the first No. 1 seed to lose to a No. 16 in the men’s N.C.A.A. tournament, Virginia left wearing a crown on Monday night.

The Cavaliers defeated Texas Tech, 85-77, in overtime for the university’s first national basketball championship, which carried with it immeasurable redemption.

“Forget last year,” Virginia’s Ty Jerome said. “This is everything you dream of since you’re a little kid.”

This title game was the first in 40 years between men’s teams that had never been there before. The last one was the showdown in which Magic Johnson’s Michigan State team beat Larry Bird and Indiana State in Salt Lake City.