Challenge accepted!
Prior to Florida last year, the last time Utah played an SEC team in the regular season was 1984 @ Tennessee (21-27 loss). They also played @ Tennessee in 1979 (18-51), @ Florida in 1977 (29-38), @ LSU in 1976 (7-35), @ Tennessee in 1975 (7-40), and @ LSU in 1974 (10-35).
So the correct answer is that the next time will be the first.