The Colts and Giants in 1958 played in the NFL’s first overtime game (Baltimore winning the championship 23-17 when Alan Ameche ran into the end zone). What teams played in the NFL’s second overtime game? It was a playoff game – the league didn’t start using overtime in the regular season until 1974. (Of course, we don’t tend to ask these kind of questions unless there’s some kind of timely reason).
The Packers and Colts, with a berth in the 1965 NFL Championship game at stake (the season before the first Super Bowl). Helped along by a controversial field goal that most believe was wide, Green Bay won 13-10 (and went on to beat Cleveland in the title game). The Colts (now doing business in Indianapolis) and Packers will play again today. Note: there was also an AFL playoff game that went to overtime, with the Dallas Texans beating the Houston Oilers 20-17 in 1962.