On November 24, 1984, with at least a share of the Southwest Conference championship on the line, the Mustangs defeated a pesky Arkansas Razorback team to finish 6-2 in the conference race. The win sealed a bid to the Aloha Bowl in Honolulu, Hawaii against Notre Dame on December 29, the Mustangs' fourth bowl appearance in five years. SMU's 31-28 victory takes it rightful place as one of the 90 Greatest Moments in SMU Football History.

Tailback Reggie Dupard contributed three rushing touchdowns and Brandy Brownlee hit three field goals as the Mustangs won a portion of the SWC title for the third time in four years. The SMU defense registered three quarterback sacks and Razorback ball carriers were trapped behind the line for 48 yards in losses.

While the defense played well, it was the offense that brought home the win. "Give the offensive line a lot of credit," said coach Bobby Collins following the game, "they have really come together the last few games." The Mustangs rushed for 222 yards on 47 attempts averaging 4.7 yards per carry. They also passed for 146 yards as the Mustangs put 31 points on the board against a good Razorback defense.

Despite spotting Arkansas a seven point lead the end of the first quarter, the Mustangs stormed back to take a 24-7 lead into the fourth quarter. However, Arkansas fought back, scoring three times in the final period. But a Don King to Ron Morris pass good for 79 yards set-up Reggie Dupard for the winning touchdown with 2:51 left in the game. The Razorbacks scored with 40 seconds left in the game, but could not convert an on-side kick. Dupard covered the kick and the Mustangs ran out the clock. The Mustangs claimed victory, 31-28.

Cornerback Roderick Jones had seven tackles, one stop behind the line and one interception, while linebacker Kit Case had 14 tackles. Noseguard Jerry Ball was named ESPN's "Defensive Player of the Game" after accounting for 13 tackles, one quarterback sack and one tackle behind the line. Keith Brooks and Reggie Phillips each added interceptions of their own.

The following week, Texas A&M defeated Texas assuring the Mustangs half of the SWC Championship. The Mustangs then went onto defeat the Fighting Irish in the Aloha Bowl to give them their second bowl victory in three years. The previous year, SMU had become the first SWC team to compile three consecutive seasons with 10 or more wins. The 1984 team extended it to four. In this four year run, SMU went 41-5-1. The 31-28 win over Arkansas for the conference title takes its place as one of the 90 Greatest Moments in SMU Football History.