The Dolphins were successful in the early 1970s, becoming the first team to advance to the AFC Championship for three consecutive seasons. They captured the AFC championship in 1971 behind quarterback Bob Griese, running backs Larry Csonka and Jim Kiick, and wide receiver Paul Warfield. The AFC Divisional Playoff Game, in which the Dolphins defeated the Kansas City Chiefs, was the longest contest in NFL history (82 minutes 40 seconds). In Super Bowl VI, however, Miami lost to the Dallas Cowboys 24–3.
In 1972 the Dolphins completed the only fully undefeated season in the NFL, winning all 14 regular season games, two playoff games and Super Bowl VII, defeating the Washington Redskins 14–7. They finished the season 17–0, and are the only team to complete an undefeated season and win the NFL title. QB Bob Griese was victim to a broken leg and dislocated ankle in Week 5 versus the San Diego Chargers and was replaced by veteran Earl Morrall for the rest of the regular season, but returned to the field as a substitute during the AFC Championship game versus the Pittsburgh Steelers and then started in Super Bowl VII. The Dolphins set the NFL single-season rushing record, and running backs Csonka and Mercury Morris became the first teammates to each rush for 1,000 yards in a season. The offensive line included future Hall of Fame members Jim Langer and Larry Little and Pro Bowler Bob Kuechenberg. The 1972 Dolphins defensive unit, called the No-Name Defense because Miami’s impressive offense received much more publicity, was the league’s best that year. It was led by linebacker Nick Buoniconti, end Bill Stanfill, tackle Manny Fernandez and safeties Dick Anderson and Jake Scott. They secured the team rushing record by averaging more than 200 yards per game on the ground for an entire season, while the defense allowed only 171 points.
Prior to the 1972 Dolphins, only the Chicago Bears, in 1934 and 1942, had finished an NFL regular season with no losses or ties. The 1934 team lost the NFL Championship Game that year to the New York Football Giants, and the 1942 team lost theChampionship to the Redskins. The Cleveland Browns were undefeated in the 1948 All-America Football Conference season.
The Dolphins finished 12–2 after the 1973 regular season and repeated as NFL champions, beating the Minnesota Vikings 24–7 in Super Bowl VIII at Rice Stadium in Houston. Miami reached the playoffs again in 1974 but lost in the first round to the Oakland Raiders, in what has entered NFL lore as the "Sea of Hands" game, considered one of the greatest games ever played. Following the 1974 season, the Dolphins lost Csonka, Kiick, and Warfield to the World Football League.