Meredith spent two years as a backup to Eddie LeBaron, eventually splitting time in 1962 before he was given the full-time starting job by head coach Tom Landry in 1963. In 1966, Meredith led the Cowboys to the NFL postseason, something he would continue to do until his unexpected retirement before the 1969 season. His two most heartbreaking defeats came in NFL Championship play against the Green Bay Packers, 34–27 in Dallas (1966), during which he was intercepted on a 4th down passing play, an interception that he later claimed was due to a coaching issue, having incorrect personnel and formation on the field, and the famous "Ice Bowl" game, 21–17 in Green Bay (1967). Already feeling physically and mentally fatigued as a leader, he had his worst playoff outing in 1968 against Cleveland Browns in the Eastern Conference Championship game, throwing three interceptions before being benched, which led to his retirement in 1969, then aged 31. His successor Roger Staubach took three more seasons to help the team win the first championship.