Doug Flutie gained national attention in 1984 when he quarterbacked the Eagles to a 47–45 win in what would be called Hail Flutie. Flutie left school as the NCAA’s all-time passing yardage leader with 10,579 yards, won the Heisman Trophy and was a consensus All-American as a senior. This was their first Cotton Bowl Classic since 1940. The Cougars shared the Southwest Conference title for the first time since 1979. By virtue of their defeat of conference co-champion SMU in their head to head meeting during the season, the Cougars were invited to play in their first Cotton Bowl Classic since 1980.
The Eagles rolled to a 31-14 lead at halftime on Flutie's three touchdown passes (to three different receivers) and a Steve Strachan touchdown, despite the Cougars' two quick ways of scoring touchdowns, one of which occurring when Larry Shepherd caught a Gerald Landry pass for a touchdown with only 22 seconds left in the half. Raymond Tate narrowed the lead with his touchdown late in the third quarter. Audrey McMillian intercepted a Flutie pass and returned it 25 yards to make it 31-27 as the third quarter came to a close. But the Eagles scored with 5:45 remaining on a Steve Strachan touchdown run. Troy Stradford sealed the game with a touchdown run with 1:06 to go as the Eagles won their first Cotton Bowl Classic ever.