In 1984, the SMU Mustangs claimed their third conference title in four years. Because of a shared title with Houston, the Mustangs traveled to Hawaii to play Notre Dame in the Aloha Bowl on December 29, 1984. The Aloha Bowl marked the Mustangs' third straight post-season bowl trip and they were determined to make the most of it. Tailbacks Jeff Atkins and Reggie Dupard did their best to shatter the Notre Dame mystique, rushing for 112 and 103 yards respectively as the Mustangs rolled up 379 yards of total offense and a 27-20 victory for one of the 90 Greatest Moments in SMU Football History.

Atkins opened the game with a 7-yard scoring run with six minutes left in the first quarter. Early in the second quarter, quarterback Don King hooked up with Cobby Morrison for a 12-yard touchdown pass to put SMU up 14-0. Notre Dame finally got on the scoreboard midway through the second quarter when Steve Beuerlein hit Alan Pinkett for a 17-yard touchdown. Irish kicker John Carney then added a field goal to move the Irish to within four points. However, the Mustangs responded when kicker Brandy Brownlee connected on an SMU bowl record, 47-yard field goal with seven seconds left in the half for a 17-10 halftime lead.

The Irish were able to shut the Mustangs out in the third quarter while Mark Brooks scored on an 11-yard run to tie the score going into the fourth quarter. Brownlee added his second field goal of the day to give the lead back to the Mustangs. Then after a defensive stand, SMU got the ball back and marched to another touchdown. This time, Dupard forced his way into the end zone from two yards out to give SMU a ten point lead. The teams played a battle of field position for several minutes before Carney brought the Irish three points closer.

Then with 2:42 left in the game, Notre Dame took possession at their own 23-yard line trailing by a touchdown. They controlled the ball for the next 14 plays setting up a dramatic finale defensive stand by the Mustangs. Desperate to get into the end zone, Beuerlein threw to the end zone on the final three plays of the game. The first two passes missed their intended targets leaving time for Notre Dame to take one more shot. Beuerlein dropped back and fired towards Pickett who was trying to break free of his Mustang defenders. However, SMU safety Tim Green got his hand up to knock away the last pass to preserve the Mustang victory.

SMU finished the season 10-2 and ranked No. 8 in both polls. It was the fourth straight season that SMU had posted 10 wins, and the third straight bowl appearance. Since the start of the 1980s, the Mustangs had compiled a record of 49-9-1, the best such stretch in school history. It was capped off by a thrilling victory 27-20 victory over Notre Dame in the Aloha Bowl for one of the 90 Greatest Moments in SMU Football History.