The 1936 Marquette squad finished the regular season with a 7–1 record after losing to Duquesne in their regular season finale. On December 9, Marquette accepted an invitation to play in the inaugural Cotton Bowl Classic on New Years Day. The appearance marked the first all-time bowl appearance for the Golden Avalanche. Marquette accepted the bid also in part to expand their brand into the Southern United States and make contacts with other southern football teams to schedule future contests.
TCU finished the regular season with a 8–2–2 record with ties against Mississippi State and SMU and losses against Texas Tech and Texas A&M. After they defeated Santa Clara in their regular season finale, the Cotton Bowl extended TCU an invitation to the game over Arkansas. On December 16, the Horned Frogs were granted permission from the Southwest Conference to compete against the Golden Avalanche in the Cotton Bowl Classic. The appearance marked the third all-time bowl appearance for TCU.
L. D. Meyer scored the first points of the game when he successfully connected on a 33-yard field goal to give the Horned Frogs an early 3–0 lead. Marquette responded with their only points of the game later in the quarter when Arthur Guepe had a punt return of 60 yards for a touchdown. After a failed extra point attempt by Ward Cuff, the Golden Avalanche led 6–3. The Horned Frogs retook the lead for good at the end of the first quarter when Meyer caught a 55-yard Sammy Baugh touchdown pass, and with the extra point led 10–6. Meyer then scored his second touchdown of the game when the second quarter when Vic Montgomery threw him an 18-yard touchdown strike. Leading 16–6 entering the second half, neither team would score again giving TCU the victory. For their performances, Ki Aldrich, Baugh and Meyer were named the Most Valuable Players of the game.