Between 1949 and 1958, SMU and Notre Dame battled each other on the gridiron eight times. When the two schools met in the 1984 Aloha Bowl, it represented their first meeting in 26 years. SMU, playing in its fourth bowl game in five seasons, scored on its first two offensive possessions. A seven-yard touchdown carry by Jeff Atkins and Don King's 12-yard pass to Cobby Morrison gave the Mustangs a 14-0 lead. Notre Dame responded with 10 unanswered points before Brandy Brownlee connected on a 47-yard field goal to give SMU a 17-10 lead at halftime.

The Fighting Irish tied the game on Mark Brooks' 11-yard touchdown run in the third quarter, but SMU regained the lead on its next possession with Brownlee's second field goal of the game. The Mustangs were able to work on the clock for most of the second half due to the strong running of Atkins and Reggie Dupard, each of whom ran for more than 100 yards in the contest. Dupard's two-yard scoring run gave SMU a 10-point lead with six minutes left in the game and the Mustangs held off a late Notre Dame rally to win, 27-20.