The Utes (10-5) dominated the Tigers (12-2) inside and ended LSU's four-game winning streak. Utah shot 67 percent in the first half and led by nine at halftime, then pulled away with a 24-5 run in the second half.
"Utah beat the living tarnation out of us, in all phases,” LSU head coach Trent Johnson said. “They are a good basketball team and they are going to have a chance to do a lot of special things during the course of the year."
Utah outrebounded LSU 37-29 and held the Tigers to seven field goals in the second half.
Johnson struggled in stopping Nevill, who hit 11-of-13 from the field, and had an easy time down on the low blocks.
"I am used to getting double-teamed, especially when I start scoring in the block,” said Nevill. “But no one came and no one helped so I just kept on going to work."
The Utes were red hot all night as they hit 60.7 percent of their shots in the second half to finish at 63.5 percent on the evening.
Carlon Brown scored 17 and Luka Drca and Shaun Green had 13 points each for Utah.
LSU returns to action on Sunday when the Tigers travel to Tuscaloosa to open SEC play against Alabama at 12:30 p.m.