Fredette reached the 30-point mark for the fourth time this season, making seven 3-pointers while hitting 12-of-25 from the field and 8-of-10 from the line.
UNLV led by as many as 10 points in the first half but the Cougars caught up by intermission and opened as much as a 21-point advantage in the second period.
It was the opening Mountain West Conference game for both teams.
Jackson Emery had 22 points for BYU (15-1) and Brandon Davies had 15.
UNLV (12-3) got 26 points off the bench from Anthony Marshall.