Fair was hit across the face on a dunk late in the first half and played much of the game with a bandage below his right eye.
Trevor Cooney had 15 points and Jerami Grant and Tyler Ennis scored 12 apiece for the Orange (5-0), who will play California in the semifinals on Tuesday.
Syracuse, which had a week off after squeaking past St. Francis (N.Y.) last Monday, has won its first five games for the sixth straight season.
Malik Smith had 16 points to lead Minnesota (5-1), Andre Hollins scored 14 and Austin Hollins had 11. The Golden Gophers, who were trying to go 6-0 for the third time in four seasons, will face Arkansas on Thursday.