Two years later, in Super Bowl V, Morrall came off the bench for an injured Unitas and kept the Colts in the game before they ultimately won on a last-second field goal.

In his first season with Miami in 1972, he came off the bench when Griese became injured early in the year, with Morrall winning all nine starts; Morrall started the first two playoff games, with Griese playing in each game before being named the starter for Super Bowl VII, where the Dolphins completed the only perfect season in NFL history.

In his more than two decades on the professional gridiron, Morrall played for six different teams, starting with his rookie year in 1956 as a first-round selection by the San Francisco 49ers, the second overall pick in the draft.

[1] On September 16, 1957, he was traded along with guard Mike Sandusky to the Pittsburgh Steelers in exchange for linebacker Marv Matuszak and two first-round draft picks.

[2] Despite the high cost of the transaction, the Steelers traded him just over a year later to the Detroit Lions in order to obtain future Hall of Famer Bobby Layne.

After spending the off-season rehabilitating from his injury, Morrall was dealt by the Lions to the New York Giants for Mike Lucci who had been acquired from the Cleveland Browns, Darrell Dess and a draft pick as part of a three-team transaction on August 30, 1965.

The team won the NFL Championship in a shutout victory but were upset in Super Bowl III against the New York Jets, where Morrall was taken out late for Unitas.

Morrall had a chance to redeem his past woes with Super Bowl V. With the Colts trailing 13–6 in the second quarter, he was tasked to step in for Unitas, who was knocked out of the game on a rib injury.

He started the Divisional Round game against the Cleveland Browns and went 6-of-13 for 88 yards while the Dolphins managed to win 20-14 (on the strength of a blocked punt returned by Charlie Babb, two field goals, and a Jim Kiick touchdown).

Together, Morrall and Griese won three postseason games (including Super Bowl VII) to complete the only perfect season in NFL history.

Over the next four seasons, he would make occasional appearances in games, starting three combined times while the Dolphins won another Super Bowl with Griese at the helm.

[13] Until first Doug Flutie and then Vinny Testaverde almost 30 years later, Morrall was the oldest quarterback to start and win a football game in the NFL.

[18] Morrall resigned as mayor to run for the Florida House of Representatives District 97 seat as a Republican in 1992 but lost the election.