Harden scored his team's first five points of the second overtime and finished with 27, making the No. 25 Sun Devils' (No. 22 AP) return to the rankings for the first time in nearly 13 years a success with a 99-90 win over California.
"It's great for us to know we can come in and get a tough win on the road," Abbott said. "We really needed that for our confidence."
Abbott hit two 3-pointers in the second extra session, a key 3 late in the first OT and yet another that tied the game with 8.1 seconds left in regulation. He finished with 25, nine rebounds and five assists to give Arizona State its 10th straight victory and fourth in a row on Cal's home floor.
It marked just the third time in school history two freshmen scored 20 or more points.
"They are playing with a lot of confidence. Our older guys have helped them a lot," coach Herb Sendek said. "Both teams played a high level of offense. We were lucky, in a hard-fought game it tilted our way. On some occasions we had to have near-perfect plays, and we did."
Jeff Pendergraph added 26 points, eight boards and four blocks for Arizona State, which has won 10 straight for the first time since an 11-game winning streak by the 1980-81 team that featured Byron Scott, Fat Lever and Alton Lister.
Arizona State (14-2, 4-0 Pac-10), in the Top 25 for the first time since ending the 1994-95 season ranked 16th, hit the road for the first time in conference play and its 4-0 Pac-10 start matches that of the 1987-88 team. The 1979-80 team began conference play 6-0.
"I thought we showed a lot of heart," sophomore Jarren Shipp said. "Ty did a great job. We had to knock down big shots and get stops. The freshmen stepped up big time on the road."
Ryan Anderson had 32 points and 15 rebounds for Cal, which got the ball under ASU's basket with 4.8 seconds to play in the first OT but couldn't capitalize when Jerome Randle missed a long 3 at the buzzer.
Harden had another spectacular second half after scoring two points and taking only two shots in the first 20 minutes. He scored 22 after the break in a 64-59 overtime victory against Arizona on Jan. 9.
Cal blamed defensive breakdowns as the difference. The Golden Bears shot 59 percent in the second half while allowing ASU to make 62 percent of its shots.
Patrick Christopher added 23 points with 5-for-7 on 3-pointers and four assists for the Bears (11-5, 2-3), who were effective against an ASU zone defense that was holding opponents to 56.7 points per game.
"Arizona State's a really good team but we definitely should have pulled it through," Anderson said. "We had them almost the entire game, momentum was with us. It's mostly our defense. We can't let down our defense in the second half and let them come back, which is what we've been doing a lot this year."
Anderson's three-point play at 12:46 put Cal up 58-57, but Harden drove the right baseline with his off hand for a powerful two-handed jam, was fouled and converted the three-point play. Abbott followed with a 3.
Cal pounded the ball inside to Anderson against the Sun Devils' zone early and he already had 12 points by the midway mark, but Pendergraph scored six straight on the other end for ASU.
Anderson, who came in leading the Pac-10 in scoring at 20.7 points, shot 12-for-14 from the free throw line and Cal attempted 27 free throws to 23 for Arizona State.
Arizona State struggled to defend Anderson's quickness in the paint in the first half and hold in check a Cal team that came in second in the conference for scoring at 79.1 points per game.
Harden -- the Pac-10's youngest player, who turned 18 on Aug. 26 -- was guarded by Christopher, Cal's top defender, and didn't attempt his first shot until a driving layin at 8:21.
Harden drew Christopher's second foul the next time down and Christopher was whistled for his third 5:03 before halftime and took a seat.
"I was disappointed we didn't get the stops we needed," Cal coach Ben Braun said. "I thought we did a great job against Harden in the first half."
Cal split its first two weekends in conference play and was coming off a 69-59 win last Saturday at Oregon State.
ASU made 12 of its first 19 shots and Abbott's 3 in the waning moments pulled the Sun Devils within 38-35 at halftime.
Cal 7-footer Jordan Wilkes missed the game after spraining his left ankle late in practice Wednesday. He was wearing a walking boot and wasn't expected to play Saturday against Arizona either.
Shake Milton scored 18 of his 20 points in the second half, and SMU pulled away in the final five minutes to beat Tulane 73-62 on Saturday night.
Zion Williamson explains why he made the decision to play for Duke and expresses his thoughts on the Blue Devils now having the top three recruits in the Class of 2018.
Jaylen Nowell scored 19 points, Matisse Thybulle added 18 points and 10 rebounds, and Washington overcame a miserable start from the field to beat Colorado 72-62 on Saturday.