Alexander was tossed for throwing a punch after the Tigers recovered a fumble by UCF quarterback Darriel Mack Jr.. Alexander punched wide receiver Gabriel Davis in the face mask.
No. 11 LSU (10-3) defeated No. 8 UCF (12-1) 40-32 to end the Knights' 25-game winning streak.
LSU was already without starting corners Greedy Williams, a first-team All-American who opted to skip the bowl game to prepare for the NFL draft, and Kristian Fulton, who missed the final two games of the regular season after undergoing ankle surgery.
Additionally, top backup Kelvin Joseph was suspended from playing in the Fiesta Bowl for a violation of team rules.
Alexander, a senior, started opposite sophomore Kary Vincent Jr. at cornerback against the previously undefeated Knights.