Nick Johnson scored 18 points and Aaron Gordon added 16 to lead the Pac 12 regular-season champions to a 68-59 victory at Viejas Arena.
Weber State came close, however.
Despite making only six of their first 30 shots and trailing by 21 with just over 10 minutes remaining, the Wildcats had a chance.
They just couldn't finish.
"Proud of our guys," Weber coach Randy Rahe said. "But it hurts. It hurts because, believe it or not, we came in expecting to win. ...
"The guys did a tremendous job. We could have pulled in the tents. But they got a little tougher and showed the resiliency they have had all year."
In the end, Arizona was just too talented, although coach Sean Miller heaped praise on Weber after his team improved to to 31-4.
"Weber State is one of the best teams we've played all season," he said. "We played some of the great teams in college basketball and I don't care what their conference is or what it says on their shirt. … In some ways, we were fortunate to advance."
Arizona's best stroke of luck came with just under two minutes remaining.
With the its lead down to 63-54 and Weber one stop away from putting severe pressure on the heavily-favored Wildcats, Johnson took the ball to the basket.
As he attempted to turn the corner, the Pac 12's Player of the Year collided with the Big Sky Conference's MVP.
Weber State's Davion Berry crashed to the floor.
The crowd inhaled … and waited.
"It was a good play," Berry said later. "I felt I beat him to the spot."
Instead, Berry was called for a blocking foul.
Arizona maintained possession and, following another foul, the Wildcats milked 1:11 off the clock.
When they finally had to shoot, Gordon drove down the lane and scored a layup that gave Arizona an 11-point lead, icing the victory.
"That's one heck of a basketball team Arizona," Rahe said. "They've got great talent [and] a great coach. They have it all. But we put ourselves in a position to [win] it down the stretch and that's what we asked our guys to do. I couldn't be prouder of them."
Weber State started quickly and took a 7-0 lead on Berry's three-point shot less than four minutes into the game. Unfortunately for the Wildcats, it was his only field goal during a 1-for-8 first half.
"I just didn't make shots," Berry said. "But I stayed with it all game long. Coach told me to keep my head up, believe and stay aggressive. ... But they play good defense."
At halftime, Weber trailed, 32-20.
It was 50-29 with 11:35 left when the Wildcats got a huge lift from freshman Richaud Gittens. He scored seven straight points, igniting the rally that gave Weber a chance in the final minutes.
"I was talking to the guys and they said, 'Be active and aggressive,'" Gittens said. "I looked at coach and he was like, 'Don't worry about it if you make a mistake. Just be aggressive.'"
Said Rahe: "We had a hard time getting easy baskets but, when he got a couple, our confidence shot up. Everybody felt, 'Maybe we can do this.' "
No. 1 Arizona 68, No. 16 Weber State 59
P Nick Johnson scores 18 points to lead Arizona past Weber State in the NCAA Tournament.
• Weber's Davion Berry finishes with 24 points after he scores just 5 (on 1-of-8 shooting) in the first half.
• After winning the Big Sky Conference regular season and postseason tournament, the 'Cats finish 19-12.