The Fiesta Bowl had been created as a bowl game for the Western Athletic Conference (WAC) champion to participate in, the first to take place for the 1971 season. The Sun Devils won their third consecutive WAC title (with an undefeated conference record for the second time in three years). This was ASU's first bowl game since 1970. Florida State was an independent in Coach Jones' first year at the program. A 5–0 start had made the Seminoles ranked #19, but later losses to Florida, Houston, and Georgia Tech knocked them out of the polls. This was Florida State's first bowl game since 1968, as they looked for their first bowl win since 1965.
Calvin Demery started the scoring when he caught a touchdown pass from Danny White to give ASU an early lead, but Florida State would tie the game with a Paul Magalski touchdown run and take the lead later in the quarter with a field goal. Woody Green took the lead back for the Sun Devils with his touchdown run in the second quarter, but FSU added a field goal to narrow the lead to one. Later in the quarter, Rhett Dawson caught a pass from Kent Gaydos (normally the wide receiver) for a touchdown to give the Seminoles the lead again, with a successful conversion attempt to make it 21–14. But the Sun Devils tied the game with a Steve Holden touchdown catch from White to make it tied at 21–21. Dawson caught another touchdown, this time from quarterback Gary Huff, to give the Seminoles the lead again, and the Sun Devils went into halftime down 28–21. The Sun Devils started off small with an Eckstrand field goal, but later in the quarter Green would give the Sun Devils once again on his second touchdown run. Florida State tied the game with a Frank Fontes field goal in the fourth quarter. Later in the quarter, Florida State punted the ball to Holden, who returned it 58 yards for a touchdown to give Arizona State the lead 38–31. But the lead would not stand as Dawson caught his third touchdown of the day to tie the game at 38. With 4:44 to play after the kickoff, the Sun Devils needed to score to win the game while giving the Noles little time, which they did as Green ran for his third touchdown of the day to give the Sun Devils the lead with :34 seconds left. The Seminoles could not muster any more magic as the Sun Devils won their second consecutive bowl game and first Fiesta Bowl. Woody Green went 101 yards on 24 carries and caught 2 passes for 41 yards for ASU, though FSU's Gary Huff was named Offensive MVP, throwing 25 of 46 yards for 347 yards, throwing two touchdowns and interceptions.
It took six years and the firing of two coaches before the Seminoles returned to another bowl game, which they did under Bobby Bowden. This was their last Fiesta Bowl until 1988. The Sun Devils went to two straight Fiesta Bowls while winning two more WAC titles and ultimately five in the 1970s.