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DALLAS (CBSDFW.COM) – “I think the greatest moment is when you win the first Super Bowl,” Hall of Fame head coach Tom Landry said, when asked about his favorite memory coaching the Dallas Cowboys from 1960 to 1988. “Everybody wants the Super Bowl.”

Landry and the Cowboys celebrated the first championship in team history on January 16, 1972.

Roger Staubach, who took over as the starting quarterback in the middle of the 1971 season, led Dallas to 10 straight victories. That included a dominating 24-3 win over the Miami Dolphins in the championship game.

It was redemption for a franchise that had come up just short of a championship for several seasons.

“A lot of fans around the country had noted the Dallas Cowboys to be a team that could not win the big game,” recalled Hall of Fame offensive lineman Rayfield Wright.

Watch: Renfro & Wright Recall Carrying Landry

Hall of Fame cornerback Mel Renfro agreed. “We had been to the bottom,” he said. “We had almost gotten to the top many times, but we finally made it. It was just an incredible feeling.”

That feeling was best defined by the smile on Landry’s face as he was carried off of the field on the shoulders of his players. “It meant everything,” Renfro recalled, “to see the photo of Tom Landry after the game. The look on his face meant everything.”

Watch: Landry’s Greatest Moment In Football

Landry agreed, saying, “I think that was the best moment I had in professional football.”

The Cowboys winning their first world championship is the greatest moment in team history.