This matchup was something of an anomaly, as it featured a rare rematch of two conference foes that had already played during the regular season. Nebraska had upset #1 ranked Oklahoma 17–14 on November 11 in Lincoln, and appeared headed towards a national championship showdown with Penn State. But unranked Missouri then stunned the #2 ranked Huskers 35–31 the following week, dropping the Huskers into a tie with Oklahoma for the Big Eight championship and knocking them out of the national championship picture.
Penn State instead faced Alabama for the national title in the Sugar Bowl, and the Orange Bowl found itself with a selection dilemma. Nebraska earned the Big Eight's automatic Orange Bowl berth by virtue of its victory over the Sooners, but, with Penn State and Notre Dame (which accepted an invitation to the Cotton Bowl Classic) off the board, the Orange Bowl committee decided to set up a rematch with Oklahoma to create the best possible matchup. This was the last time a non-championship postseason bowl featured two teams from the same conference until the 2015 Arizona Bowl.
Nebraska scored first on a 21-yard touchdown pass from Tom Sorley to Tim Smith giving Nebraska a 7–0 lead. Oklahoma tied the score on a 3-yard scamper by Heisman Trophy winner Billy Sims, and then went ahead when Thomas Lott scored on a 3-yard touchdown run to take a 14–7 lead into the locker room.
The revenge-minded Sooners then took control. In the third quarter, Sims scored his second TD on an 11-yard touchdown run. Both sides traded field goals before Lott scored on a 2-yard touchdown run, increasing Oklahoma's lead to 31–10.
Nebraska rallied late, with Rick Berns scoring on a 1-yard touchdown run, and then Sorley threw a 2-yard strike to Junior Miller, but by then the game had ticked down to its final seconds, as OU prevailed 31–24, to finish the season 11–1, avenging its only loss of the 1978 season. Nebraska finished 9–3.