"You don't want to think of the consequences of losing because you don't plan on losing," said Alford, who had 10 points. "We believe we can beat anybody and we've just got to show up and play like we can, and tonight we did that."
The Bruins (14-11, 5-7 Pac-12) had lost to Arizona on Friday, their fifth loss in seven games. They bounced back against the Sun Devils (14-12, 4-9), shooting 49% from the field.
Isaac Hamilton and Prince Ali each had 12 points for the Bruins.
"This was a great road trip for us," Coach Steve Alford said. "We played really well, really well for 70-80 minutes, even in Tucson."
Arizona State was coming off a victory over USC on Friday and kept up with the Bruins in the first half behind its three-point shooting.
"I felt like we were on the verge of something after Friday night and, like has happened most of the year, there's progress and there's regression," Coach Bobby Hurley said. "We regressed again tonight."
The Bruins, who beat Arizona State at home this season, had another solid first half, making 16 of 33 shots. Alford had nine points and six assists iin the first half, helping UCLA lead, 37-35.
Arizona State made seven of 13 three-point shots in the half, including three by Kodi Justice.
"We knew taking away the three was really important and it kind of got away from us in the first half so it was a close game," Bryce Alford said. "Second half, I thought we did a better job contesting."
The Sun Devils missed eight of their first 10 shots in the second half and the Bruins pounded the ball inside to Tony Parker (six points) and building an eight-point lead.
The Bruins kept making shots and Alford kept getting assists, leading to an 11-1 run that put UCLA ahead, 69-54, with about five minutes to play.
Arizona State continued to struggle around the rim and relied even more on three-point shots.
"We were missing wide-open shots, layups and the next thing you know we're down 13 points and trying to battle back," said Justice, who finished with 12 points. "They're a good team. It's hard to battle back against a team like that."
Andre Spight scored 21 points, and Obinna Oleka had 14 points and 13 rebounds for Arizona State.