For the second round in a row, it came down to a last play.
And for the second game in a row, it went Arizona's way.
Down two, Williams had his first chance to be a hero with just under 15 seconds left, but was unable to hit the shot.
However, the Wildcats forced a five-second violation and got a second breath.
Williams then took advantage of his second opportunity, receiving a great pass from Kyle Fogg to hit the shot and go to the line.
The made free throw gave Arizona the one-point lead and Texas was unable to convert, putting the UA in the Sweet 16.
Williams shot 4-15 from the field and only went 9-15 from the line.
He did, however, come big at the end of the game and that is what will likely be remembered.
In addition, Solomon Hill may have played the best game of his career, finishing with 16 points and eight rebounds.
Not to be outdone, Jordin Mayes played his second great game in a row, also finishing on 16 points and only missing one shot from the field.
The Longhorns were led by 23 points from J'Covan Brown, but were unable top win the game on his attempt layup with no time left on the clock.
Arizona will now face Duke on Thursday.
Wildcat Authority Top Stories
10/19 Football Notebook: Arizona's Bye WeekRich Rodriguez discusses bye week practice, quarterbacks, and more.
Wildcat AuthorityYesterday at 9:10 PM
Authority Report: Does UA lead for Graham?This week's Authority Report discusses Thomas Graham's recruitment and more.
Wildcat AuthorityYesterday at 8:50 PM
Ira Lee is a WildcatIra Lee has committed to Arizona. Read on for the latest.
Wildcat AuthorityYesterday at 11:14 AM
Dylan Smith taking on unique roleDylan Smith is comfortable with his new team. Read on to see what his role is and more.
Wildcat AuthorityTuesday at 9:04 PM