Fair's basket broke a 55-55 tie and the Orange hung on for the win as Cincinnati's Cashmere Wright and JaQuon Parker each missed 3-point attempts in the closing seconds.
Michael Carter-Williams provided 16 points, seven assists and five rebounds for Syracuse (18-1, 6-0 Big East), which erased a seven-point deficit over the final 6 minutes and posted its Division I-best 35th consecutive home victory.
Fair and Brandon Triche supplied 13 points apiece in the victory.
Sean Kilpatrick put in 21 points and grabbed five rebounds for the Bearcats (16-4, 4-3), who shot just 32.7 percent from the field in the loss.
Celebrity Breakups and divorces of 2014 [PHOTOS]