The three-time captain, who had been shooting worse than 30 percent from the floor, dropped 22 points on the Utes, including four free throws in the final 30 seconds to seal a 53-48 win for BYU at the Huntsman Center.
"She just seems to have our number," Utah coach Anthony Levrets said of the point guard. "That happens in rivalry games sometimes."
Steed said she knew she would have to take more shots after leading scorer Lexi Eaton went down last week with a season-ending knee injury.
"She was kind of our aggressor on offense," Steed said. "She was the one that got to the rim and got to the free-throw line for us. All of us have to do a better job."
A poor shooting performance also helped doom the Utes. The team shot just 25.5 percent from the floor for the game.
"We just didn't knock down shots today," Levrets said. "We are a really, really good shooting basketball team and, for whatever reason today, the ball didn't go in the basket."
Utah (7-1) trailed by seven after the first half and spent the final 20 minutes chipping away at BYU's lead. When junior forward Taryn Wicijowski fired a shot from the top of the key that bounced around and seemed to come to a complete stop on the lip of the rim before rolling through the net to give the Utes a 48-46 lead, the crowd of 1,925 at the Huntsman Center erupted.
Steed missed a jumper on the next trip down the floor, but center Jennifer Hamson was there for a rebound. BYU's Stephanie Vermunt Seaborn quickly made a 3-pointer to give the Cougars (5-4) the lead for good.
Hamson would not have been available had BYU's volleyball team not lost Friday night in the NCAA Tournament in Nebraska.
Hamson consistently drew double teams from the Utes in her 21 minutes on the floor, opening up shots for Steed and the rest of her teammates. She also gave BYU another body to wear down the Utes' Wicijowski and Michelle Plouffe in the post.
Wicijowski tied a career high with 16 points, and added 15 rebounds despite playing on a badly sprained ankle. But her points came on 5 of 15 shooting.
Plouffe scored 16 points on 4 of 17 shooting.