Barefield scored six points in overtime, and his 3-pointer for a 79-76 lead with 2:40 remaining was the last basket either team scored.
He made a free throw with 3.4 seconds remaining, and Arizona State's Tra Holder had his desperation 40-footer at the buzzer fall well short.
Justin Bibbins scored 15 points on five 3-pointers and Tyler Rawson had 15 points and nine rebounds for the Utes (13-7, 5-4 Pac-12). Utah has won three in a row after losing the previous four.
Holder had 23 points and 10 rebounds, and Shannon Evans II had 14 points and seven rebounds for the Sun Devils (15-5, 3-5). Arizona State was the last undefeated team in NCAA Division I at 12-0 before entering conference play.
Barefield, a former starter who has come off the bench the past two games, sent the game into overtime at 69-69 on a 3-pointer with 1.8 seconds remaining.
After Barefield's fourth trey gave the Utes a 79-76 lead, Mickey Mitchell hit one of two free throws on Arizona State's next possession.
Utah had three turnovers and missed 3 of 4 free throws the rest of the way, while Arizona State missed its final six field-goal attempts.
Arizona State reserve guard Remy Martin scored all 10 of his points in a 13-0 second-half run as the Sun Devils took a 60-55 lead they could not hold.
Holder made a driving layup for a 67-66 lead with 54.1 seconds left in regulation, and Evans a made a driving layup with nine seconds remaining before Barefield's 3-pointer tied it.
De'Quon Lake had 10 points for the Sun Devils.
Bibbins made 5 of 13 3-point attempts and had six assists before fouling out late in regulation. He is the reigning Pac-12 player of the week after recording two double-doubles in a sweep of the Washington schools last week.
Utah made 14 of 32 3-point attempts and shot 43.5 percent from the field.
Arizona State shot 40 percent overall, 36.4 in the second half, and finished 10 of 27 from 3-point range.
--Field Level Media
Utah | Arizona State | |
Sedrick Barefield 17 | Scoring | Tra Holder 23 |
Justin Bibbins 6 | Assists | Tra Holder 4 |
Tyler Rawson 9 | Rebounds | Tra Holder 10 |
Jayce Johnson 5 | Free Throws Made | Tra Holder 7 |
Gabe Bealer 2 | Steals | Remy Martin 2 |
Jayce Johnson 3 | Blocks | Kodi Justice 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Utah | 80 | 43.5 | 14-32 | 12-18 | 19 | 36 | 5 | 6 | 12 |
Arizona State | 77 | 40.0 | 10-27 | 11-14 | 14 | 43 | 2 | 6 | 10 |