The 43-year-old Miller went 16-15 last year in his first season at Arizona, where the successes of the former coach Lute Olson still loom large. Olson led the Wildcats to their only national title in basketball in 1997, and the revival under way under Miller has Arizona hoping a second could be coming.

Arizona is in the Round of 8 for the first time since 2005, and will face third-seeded Connecticut on Saturday largely because of its furious finish on Thursday night. After trailing by 6 points at halftime, Arizona outscored Duke by 55-33 in the second half, when the sophomore forward Derrick Williams finally got the assistance he had not received before the break.

Williams had 25 of his 32 points before the intermission, but Arizona used a 28-9 run early in the second half to break open the game. The sophomore guard Lamont Jones scored 14 of his 16 points in the second half, and Solomon Hill added 10 of his 13.

“I really felt like it was two different games,” Miller said. “In the first, Derrick’s individual play allowed us to have a chance. In the second half, we were revved up and we really rebounded the ball. That was the difference in the game.”

After coming close to elimination in a Round of 32 win over Michigan, Duke did not escape again. It took almost every one of Nolan Smith’s 24 points to help Duke Coach Mike Krzyzewski win his 900th career game against the Wolverines, but Smith, a senior guard, failed to repeat the performance against the Wildcats. He scored only 8 points on 3-of-14 shooting.