The junior, whose previous best was a 9.85, earned the mark even though she was competing second in the lineup.
Normally judges are a little conservative in their scoring early on, so they have room to reward the more difficult routines later in the lineup.
However, Del Priore's routine was flawless.
"I knew I nailed every pass and I worked hard on it this week," she said. "It finally clicked."
Her perfect mark was the first on the floor since Annabeth Eberle earned one in 2005. Two weeks ago, Tory Wilson earned a 10.0 on the vault for Utah's first perfect mark since Ashley Postell earned 10.0s on the vault and balance beam in 2008.
Del Priore joined the floor lineup after Corrie Lothrop tore her Achilles tendon and was lost for the season. She earned scores of 9.7, 9.75 and 9.775 leading up to Saturday's performance.
"It's awesome," she said of competing. "I finally get my spot and earn my spot every week."
Del Priore also had a career best 9.9 on the vault. She was thrilled with that effort and never imagined it might be overshadowed by something even better less than an hour later.
"I am really pleased for Lia," Utah coach Greg Marsden said. "She has worked so hard and to put her in that position and get that scored, it was thrilling for all of us."
Streak still alive
Wilson extended her vault winning streak to seven meets, although she had to share the title Saturday.
Wilson, who scored a 10.0 on the vault last week, was deducted for just a slight separation of her feet on her landing.
The effort was enough to notch the 9.95. Minutes later, Stanford's Nicole Dayton matched it with a similar landing.
The last gymnast to win seven vault titles in a row was Kyndal Robarts in 2010. Postell won nine in a row in 2008.
Stanford's Ashley Morgan won the all-around with a 39.45. … Utah's Nansy Damianova tied her career best 9.9 on the vault and 9.925 on the floor. … The Utes compete at BYU on Friday.