LSU won the evening session with 198.125, followed by Florida (197.7125) and Alabama (197.6) while Nebraska (197.2125), Michigan (196.4625) and Georgia (195.8) all missed the cut.
The Super Six begins at 7 p.m. MDT and will be televised by ESPNU.
Advancing to the finals was redemption for the Utes, whose 2016 campaign ended in disappointment when they suffered two falls and a bad dismount on the balance beam to slip to ninth.
On Friday, the balance beam proved again to be the pivotal event, but this time everything went Utah's way.
The Utes were in fifth after mediocre showings on the vault and uneven bars, a situation that could have been prime for a young team like Utah's to disintegrate under pressure.
Instead the Utes conquered the beam in a fashion few Utah teams have done of late. The Utes earned a 49.3875 on the beam, their fourth-highest beam score of the year. The effort moved them past Washington and Denver into third.
Utah clinched its spot in the Super Six with a 49.4875 on the floor, also the fourth-highest score of the season.
With Oklahoma the heavy favorite to win, the Utes can go into the Super Six with no pressure.
"We are the underdogs, but we have been the underdogs all season," senior Baely Rowe said. "We have taken that fire, and we want to prove everybody wrong. It's a good spot for us to be in. We can compete and see what we can do."
The Utes earned that underdog status after losing top gymnasts Sabrina Schwab and Kim Tessen to season-ending injuries in January. They were dealt another challenge when Kari Lee suffered a high ankle sprain before regionals which has limited her to the uneven bars.
The Utes' tenacity that has been the trademark of 2017 was never more present than Friday when they made their comeback on the balance beam.
Maddy Stover keyed the effort with a season high tying score of 9.85 in the leadoff spot. MaKenna Merrell followed with her season high of 9.9 and MyKayla Skinner scored 9.9125 to lead the team.
The Utes said they didn't know where they stood in the team standings, but felt things shift in their favor after the beam.
"For me personally, that was the best beam set I've done," Stover said. "I wanted to be aggressive and get the ball rolling for us to have a great beam set. We caught fire and that pushed us through."
Utah co-coach Megan Marsden, who coaches beam, called the effort "heartwarming," particularly after what happened a year ago.
"It helps to do it over and over again, and we have had a lot of good beam performances this year," she said. "Today was representative of what they can do."
Co-coach Tom Farden called the meet a tale of two halves, noting the change in the team's attitude in the last two events.
"We were trying to guide their gymnastics too much," he said. "We said we had to loosen up and get back to being our normal selves and get back into our routines and rhythm, and we did."
Now that they've made the Super Six, the Utes can feel less pressure, Merrell said.
"It was so exciting to see our hard work pay off after we struggled on beam," she said. "We redeemed ourselves. Tomorrow we can just leave it out on the floor."
NCAA Gymnastics Championships
P At Chaifetz Arena, St. Louis
When • 7 p.m. MDT TV • ESPNU
Teams • LSU, Oklahoma, Florida, Alabama, UCLA, Utah.
Inside • Utah freshman MyKayla Skinner ties for the national title in the floor exercise. > C6