Randle's jump shot with 3½ minutes left gave the Cardinal a 52-49 lead. The Huskies pulled within a point when Daniels tipped in a missed 3-point attempt by Niels Giffey.
But Shabazz Napier missed three shots in the final 40 seconds with a chance to put the Huskies ahead. He gave up an opportunity on UConn's final possession, passing the ball to Omar Calhoun, whose 3-pointer from the right wing bounced off the rim.
Stanford came in 0-4 against UConn and had not beaten a Top 25 team away from Palo Alto since the 2008 NCAA tournament.
The Cardinal's previous seven wins came over teams that were a combined 32-41.
Napier, who finished with 12 points and eight assists, missed two 3-pointers on a key possession with the Huskies trailing 52-51. Stanford got the ball back with 28 seconds left after a scrum underneath the basket.
Napier fouled Huestis on the inbounds play and he hit one of two foul shots.
Napier, who beat Florida with a jumper at the buzzer earlier this month, missed another shot with 8 seconds left, forcing UConn to foul again.
He got the ball back on a rebound after Huestis missed another free throw attempt. He dribbled down the court, but instead of trying a shot, he passed to Calhoun.
No. 12 Baylor 91, Northwestern State 84 (OT) • In Waco, Texas, Kenny Chery scored 12 of his 20 points in overtime and No. 12 Baylor returned from an extended break with a win over Northwestern State.
Chery had a steal in the first minute of overtime after Sabri Thompson lost control of the ball. Chery picked it up and drove to make a tough short jumper while being fouled. He shouted out while still sitting on the court after the ball went through the hoop to put the Bears (9-1) ahead to stay. He added the free throw.
Texas 86, No. 14 North Carolina 83 • In Chapel Hill, N.C., Demarcus Holland scored on a stickback of his own free throw with 4.1 seconds left to help Texas hold on and beat North Carolina.
Holland finished with 15 points for the Longhorns (10-1), who survived a missed 3-pointer from UNC's Marcus Paige on the final play to earn their sixth straight win.
Isaiah Taylor scored 16 points to lead Texas.
• No. 3 Ohio State 76, Delaware 64
• Stanford 53, No. 10 UConn 51
• No. 12 Baylor 91, Northwestern St. 84 (OT)
• Texas 86, No. 13 North Carolina 83
• No. 22 UMass 83, Ohio 71
• No. 24 San Diego State 76, Southern Utah 39