Nick Johnson made six free throws in the final 25 seconds, and the Wildcats (11-0) held on for a 72-70 victory after rallying from an 11-point deficit in the second half.
Arizona received all but two of the first-place votes from the 65-member national media panel.
Syracuse (10-0) got the other two No. 1 votes and remains second in the poll, with the top eight teams holding the same spots from last week.
The Orange also were tested this past weekend, as C.J. Fair hit three big shots from the right baseline in the second half to help Syracuse hold off St. John's 68-63 on Sunday at Madison Square Garden.
Kentucky, the preseason No. 1, dropped from No. 11 to 19th with its third loss of the season -- all to teams ranked in the top 14 in this week's poll.
The Tar Heels' 82-77 victory moved them from No. 18 to 14th. North Carolina is the only team with three wins over ranked teams. The Tar Heels also beat then-No. 3 Louisville and then-No. 1 Michigan State.
Kansas, which lost to Florida last week before beating New Mexico, dropped five spots to 18th, the Jayhawks' lowest ranking since they were 21st in February 2009. The Gators moved up three spots to No. 16.
There are two games between ranked teams this week.
On Tuesday, No. 15 Memphis and No. 16 Florida meet in the Jimmy V Classic at Madison Square Garden. On Saturday, No. 7 Oklahoma State and No. 20 Colorado meet at the MGM Grand Garden Arena in Las Vegas.
The Associated Press contributed to this report.