Park City had been struggling mightily from the line all night, and team leader Carson Lyman had fouled out of the game moments before.
Mayo, however, rose to the occasion, knocking down both free throws to lead her team to a 47-46 victory.
"She thrives on the pressure," Park City coach Sam White said. "When the lights are on, she steps it up."
White added that he was proud of his team's resilience in the hard-fought battle.
"It got a little sloppy," he said. "But they found a way. I can't say enough about Carson's leadership."
Lyman, who had already scored eight points in the fourth quarter, fouled out of the game by fouling an opponent to preserve as much time as possible for her teammates to mount a comeback.
"That kept us in the game," White said.
Additionally, he said, his team did a good job of handling Uintah's pressure defense.
"They did a great job breaking the press, being confident, and getting the best shots they could out of it."
The Miners improved to 4-7 overall (2-2 region) with the win. They were back in action Tuesday night at Judge Memorial after this issue went to press. They'll also play Friday night at Wasatch.