Barrera's clinching single to center was her second hit off Wildcats ace Danielle O'Toole.
After a second-inning leadoff single from Kelly Martinez, it wouldn't be until the seventh inning when Utah would get on base with another single again, from Martinez, who moved to second on a groundout by Delilah Pacheco, setting up Barrera's game-winner as pinch-runner Ryley Ball raced home and beat the throw by Arizona center fielder Alyssa Palomino.
"We had the momentum, I know we did. We were having good at-bats the whole game," Barrera said. "I mean, the game would pay us back with something falling in a hole or something getting through, because we were putting good swings on her pitches."
"What's really fun for me is the two freshmen there in that last inning," Utah coach Amy Hogue said. "Alyssa and Kelly were the difference-makers. Those two are so big for us in our lineup this year."
The Utes went up 2-1 in bottom of the first after the Wildcats tallied one in the top of the frame. That first rally for Utah included four hits, capped by an RBI bloop single by Bridget Castro.
Arizona tied the game in the top of the second as a throwing error led to Tamara Statman crossing the plate to tie the score at 2.
Utah switched pitchers in the middle of the game when Miranda Viramontes relieved starter Katie Donovan in the fourth.
Viramontes got out of a bases-loaded jam thanks to a groundout to keep the score tied.
"These series are really helping this team to get a feel for what postseason is going to feel like," Hogue said.
R Alyssa Barrera singles to center to score the winning run in the seventh after Kelly Martinez started the rally with a single to right-center.
• Delilah Pacheco, Barrera, Hannah Flippen and Bridget Castro single during a two-run first inning.