Wyoming trailed for most of the first half, rallied to lead by 10 in the second period, then fell behind by seven points with 2:30 to play. The Cowboys came back again to take a one-point lead when Josh Adams made two free throws with 8 seconds left.
Elorriaga, however, hit his clutch jumper for the last of his 18 points in the opening Mountain West Conference game for both teams.
The Cowboys had won their first 13 games of the season and their loss leaves Arizona, Michigan and Duke as the only unbeaten teams remaining in major college basketball. Boise State improved to 13-2.
Anthony Drmic also scored 18 points for the Broncos and Igor Hadziomerovic added 11. Boise State made 11-of-19 from 3-point range.
Wyoming was led by Darrious Gilmore with 17 points.