With No. 1 ranked Michigan State falling to North Carolina, Arizona (9-0) seems a safe bet to move to No 1.
"I think it's something we feel like we've earned," Wildcats coach Sean Miller said. "We know that being ranked No. 1 doesn't mean that we won the championship or the season's now over, but I'm not going to play the negative card at all. ... To be ranked No. 1 is maybe the greatest compliment you can have."
Bryce DeJean-Jones scored 16 points, Khem Birch had 12 and Roscoe Smith 10 for the Rebels (3-4) in their first road game of the season.
Smith entered the game as the top rebounder in the country at 16 per game. He finished this one with six rebounds, just one on offense as Arizona outrebounded UNLV 41-29, 18-5 on the offensive boards.
"There were times I felt that I was boxing out three guys," Smith said. "Arizona is ranked No. 2 and now will be No. 1, so they didn't' just get there with no one."
There were 18 lead changes and neither team led by more than six points.
McConnell sank a 15-footer with 3:10 to play to put Arizona up for good, 58-57. After Dejean-Jones missed a 3-pointer, McConnell's pretty bounce pass to Rondae Hollis-Jefferson for a dunk made it 60-57 with 2:20 to play.
UNLV managed one field goal in the final six minutes, Birch's rebound basket that gave the Rebels their last lead at 57-56 with 3:30 to play.
Birch made one of two free throws with 1:52 to go to cut Arizona's lead to 60-58, but McConnell found Ashley for a basket with 27 seconds to go to make it 62-58. McConnell made one of two free throws with 15.3 seconds to go to wrap up the scoring.
"He's in many ways the heart and soul of what we do," Miller said, "and I think you saw that in many ways in the second half."
McConnell said he "just tried to slow the game down, let it come to me."
"I kind of live for those moments," he said, "and I know we all do."
There were 30 turnovers in the game, 16 by UNLV and 14 by Arizona.
The Rebels shot 64 percent in the first half (16 for 25) to Arizona's 52 percent (17 of 33) and led 42-39 at the break.
The scoring dropped drastically in the second half, with Arizona outscoring UNLV 24-16. The Rebels shot 28 percent (7 for 25) in the second half while Arizona was at 32 percent (11 of 34).
Miller said that was the emphasis at halftime, to get back to his team's identity -- defense and rebounding.
He praised the UNLV effort, saying he saw a bunch of talented players playing together as a team. That's the way Rebels coach Dave Rice saw it, too.
"We were a confident group coming in here and we felt we had a great week of practice," Rice said. "We spent most of this season getting to know one another and we have made major strides."
There were 19 turnovers in the first 20 minutes, 10 by UNLV and nine by the Wildcats. Every one of the seven Arizona players who played in the first half had at least one turnover.
The Wildcats led 37-31 on McConnell's reverse layup on a pass from Hollis-Jefferson with 3:35 to play. Arizona was up 39-35 on Hollis-Jefferson's spin move inside with just under two minutes to go, but Roscoe Smith sank a 17-footer, Kevin Olekaibe hit a 3 and Kendall Smith scored on a reverse layup to give UNLV its three-point halftime cushion.
Arizona scored the first six points of the second half to go up 45-42, but the Rebels scored the next six to lead 48-45 on Dejean-Jones' 16-footer with 15:36 to play.
A 5-0 spurt regained the lead for Arizona, Aaron Gordon's emphatic dunk on a pass from Ashley made it 52-49 with 12:05 to go. Again, the Rebels responded, scoring the next six and the back-and-forth battle persisted.
The capacity crowd at McKale Center was decked out in white for the team's annual "white out" promotion. Arizona had lost its previous two white outs, and this one was shaky.