Ameche may be best remembered for his role in the 1958 NFL Championship Game at Yankee Stadium, often cited as "The Greatest Game Ever Played." Ameche scored the winning touchdown for the Colts on a one-yard run with 6:45 left in overtime as the Colts beat the Giants, 23–17. It was his second touchdown of the day as he also scored a touchdown on a 2-yard run in the second quarter. His overtime touchdown was the last in championship history until Super Bowl LI in February 2017, when James White scored at 3:58 of overtime as the New England Patriots beat the Atlanta Falcons, 34–28.