Radenovic scored 16 points in the first half as Arizona (20-9, 11-7 Pac-10) built a 20-point lead. Radenovic tried to hold Stanford (18-11, 10-8) off, scoring all nine Wildcats points in a nearly eight-minute stretch late in the second half.
Kenny Brown provided a big spark for Stanford after starting point guard Mitch Johnson was unable to play in the second half because of food poisoning. Brown scored 17 points after halftime, including a game-tying 3-pointer from the corner with 6.1 seconds to go in regulation.
But the Cardinal could never get the lead in overtime, with their best chance coming when Brook Lopez made only one of two foul shots with Stanford down by one with 1:53 to go.
Radenovic answered with a basket inside to put Arizona up 80-78. He then added four free throws down the stretch to ice the game for the Wildcats.
Marcus Williams added 15 points and Mustafa Shakur had 10 for Arizona, which must wait to find out its seeding in the upcoming Pac-10 tournament. The Cats will play Thursday at 12 noon PST in Staples Center in Los Angeles.
Lopez scored 21 points and Lawrence Hill added 20 for Stanford, which will be the sixth seed in the conference tournament. But the Cardinal figure to be a good bet to make the NCAA tournament based on their winning record in the Pac-10 and five wins against ranked opponents.
Stanford trailed by 19 at halftime but rallied back with a 15-4 run early in the second half to cut the lead to single digits for the first time since the opening minutes. Hill's 3-pointer with 10:29 to go capped the run and cut Arizona's lead to 53-45.
Chase Buddinger hit a 3-pointer to slow Stanford's charge, but the Cardinal kept creeping closer and cut the lead to four on Lopez's leaner with 7:35 to go.
Radenovic answered with a three-point play and then a jumper to put Arizona back up 65-56 with 6:36 to go. Stanford got it down to four again a minute later, but once again Radenovic responded with a driving basket.
The Cardinal never led in the game and didn't tie it until Brown's 3-pointer in the final seconds.
The Cardinal, already playing without second leading scorer Anthony Goods, were hurt even more by a bout of food poisoning that hit starters Mitch Johnson and Fred Washington, as well as three reserves this week.
Johnson and Washington needed intravenous fluids before the game just to be able to play. Both players struggled, scoring just two points for the game. Johnson sat out the entire second half.
Jawann McClellan missed the game for Arizona after injuring his left shoulder in practice Friday.
The Wildcats scored on their first eight trips down the court to take an early 15-point lead. Their only miss in the first 6 minutes was a jumper Brett Brielmaier that Radenovic rebounded.
Radenovic then hit a 3-pointer on the trip, as he scored the final seven points of a 15-0 run that gave Arizona an 18-3 lead.
The Cardinal missed 16 of their first 20 shots and were being outscored 16-13 by Radenovic over the first 15 minutes. The frustration got to coach Trent Johnson, who was called for a technical foul with 9:15 remaining in the half. That failed to spark the Cardinal, who went into the break trailing 41-22.
The victory gave Arizona its 20th consecutive 20-win season dating to his 1988 Final Four team that finished 35-3.