SAN ANTONIO -- If winning college basketball is about learning and adjusting and then executing, fifth-seeded Houston did more than ace its test against top-seeded Arizona in the teams' NCAA Tournament Sweet 16 heavyweight battle on Thursday in San Antonio -- it earned its way onto the honor roll.

Jamal Shead poured in 21 points and Kyler Edwards added 19, including a huge 3-pointer with 1:26 to play, as the Cougars waylaid the Wildcats 72-60 in the South Region semifinals.

The Cougars (32-5) will play second-seeded Villanova on Saturday in the Elite Eight. Villanova beat 11th-seeded Michigan 63-55 in the first South semifinal Thursday.

Houston never trailed, earning a six-point lead at halftime via its defense and holding off the deeper Wildcats in the second half with timely 3-pointers from Shead and Edwards.

"Once we come out of the locker room, we feel like we're supposed to be there at all times," Shead explained. "We're always feeling like we're the toughest team out there."

Arizona got to within two points twice in the first 6 1/2 minutes, but the Cougars shrugged off the Wildcats, eventually building a 61-49 advantage after two free throws by J'wan Roberts with 7:10 to play.

The Wildcats closed the gap to six points with 2:12 remaining before Edwards produced his back-breaking 3-pointer to all but cement the win.

"I thought tonight, we were solid -- we weren't good or really good," Houston coach Kelvin Sampson said. "Good, bad or indifferent, every team is known for something. All our teams eventually get there. You know, it's not always smooth sailing. We're not going to win a lot of beauty contests. But victories don't come with asterisks.

"Our team is a tough bunch. We've gotten a lot better as the season's gone on. But all the credit goes to these kids."

Josh Carlton added 10 points for Houston. The Cougars held Arizona to 33.3 percent shooting.

Dalen Terry paced Arizona with 17 points, with Bennedict Mathurin adding 15 and Christian Koloko scoring 10 for the Wildcats (33-4).

Houston swarmed the Wildcats in the first half, holding Arizona to 28 percent shooting while building a 34-28 lead at the break. The Cougars roared to a 14-4 lead six minutes into the game after a driving layup by Edwards that capped a 7-0 run.

The Wildcats closed to within four points on two occasions, the latest via a pair of free throws by Terry with 7:01 to play in the half.

Houston stretched the margin back to 10 points and was up 34-26 before two free throws from Koloko with 0.6 seconds left brought Arizona to six points at halftime.

Shead, Edwards and Carlton scored six points each to lead a balanced Cougars attack in the half. Houston shot 44.8 percent despite making just 3 of 12 shots from beyond the arc. But the Cougars ruled the lane, scoring 18 points in the paint.

Arizona was paced by Terry's eight points before halftime; the Wildcats made more 3-point shots (4) than two-point baskets (3) in the half.

Every time Arizona made a run, the Cougars counterpunched. When the Wildcats went to a pick-and-roll style offense to jump-start its attack in the second half, Houston changed defenses to counter that strategy.

"Houston is great defensively, and they are a hard team to make a run on because of their offensive rebounding," Arizona coach Tommy Lloyd said. "We ran into a really good team tonight. They were just a little bit too much for us.

"We really built some foundational pieces this year that are going to really serve us well moving forward. I'm extremely proud of the guys, extremely proud of the coaching staff."

--Steve Habel, Field Level Media