The Wildcats (3-0 Pac-12) blew a 13-point lead with 6:16 to play and committed a season-worst 17 turnovers. UCLA shot 41 percent in the second half against a team that had been holding opponents to 36 percent in the final 20 minutes.
"Losing to them three times last year definitely made us more hungry," said Gabe York, who had 12 points. "None of us forgot that."
Johnson added: "It was definitely a chip on my shoulder."
Kaleb Tarczewski made all six of his field goal attempts and scored a career-high 16 points for the Wildcats in the lone regular-season meeting between the longtime conference powers.
The 1931-32 Wildcats also began the season 16-0.
Freshman Zach LaVine hit a 3-pointer that got UCLA to 77-75 with 15 seconds left, but he missed another one with 2 seconds to go that would have left the Bruins down one.
Kyle Anderson had 16 points and 11 rebounds, and Jordan Adams added 12 points and a career-high 11 rebounds for the Bruins (12-3, 1-1). They haven't beaten a top-ranked team since March 13, 2003, when they took down Arizona in overtime in the Pac-12 tournament.
No. 24 Memphis 73, No. 12 Louisville 67 • At Louisville, Ky., Joe Jackson and Shaq Goodwin each scored 15 points and Memphis rallied late for an upset of Louisville.
Geron Johnson added 13 points, Chris Crawford 12 and Austin Nichols 10 as all five starters scored in double figures to help the Tigers end a four-game losing streak to the defending national champions.
• No. 1 Arizona 79, UCLA 75
• No. 24 Memphis 73, No. 12 Louisville 67
• No. 17 Oregon vs. California, late
• No. 20 Iowa 93, Northwestern 67
• No. 22 Gonzaga vs. Portland, late