Lee earned 9.85 on the vault, 9.825 on the bars, 9.9 on the beam and 9.875 on the floor while Skinner totaled 9.875 on the vault, 9.825 on the bars, 9.8 on the beam and 9.925 on the floor.
Saturday marked the first time Lee has performed in the all-around this year as the Utes have held her out of floor while she recovered from the torn Achilles tendon she suffered in January 2016.
Her win proved to be the bright spot for the Utes, even if it prevented Skinner from setting a record.
"She was obviously the highlight for us," coach Tom Farden said. "She was pressing during warmups a bit and I told her to stop trying to be too perfect and just do her gymnastics and she would be fine."
Lee didn't realize she had beaten Skinner and was surprised at her finish.
"She is a force to be reckoned with," she said of Skinner. "You don't think about beating another teammate, you are just trying to get through your routines."
Farden was disappointed the Utes lost, but said the small mistakes were just too much to overcome.
"We got tight on bars and we weren't as aggressive as we wanted to be," he said.
On bars, leadoff MaKenna Merrell fell and scored 9.075. The Utes never really found their form on the event, scoring 49.025, their third-lowest score of the season on the event.
On floor the normally consistent and high scoring Tiffani Lewis fell, scoring just 9.35. Without her usual effort the Utes logged just 49.25, the third-lowest score of the season on that event.
Utah wasn't its normal self on the vault, either, totaling just 49.125, its second-lowest mark of the season.
Despite the mistakes, the Utes trailed Georgia just 147.65-147.4 going into the final rotation. But Georgia, fueled by a large home crowd and the emotion of senior night, soared to the win with a 49.6 on floor.
The Utes totaled 49.25 on the balance beam.
Stegeman Coliseum has been the most difficult place for the Utes to be successful as they hold a 3-12 record in the arena. The last time the Utes won there was in 2011.
"It was a hostile environment and a tough place to compete," Farden said. "But we never gave up and we kept the pressure on them."