Of course, he chose to sign with the Dallas Cowboys and would start one game as a rookie. He primarily backed up starting quarterback Don Meredith. As a rook, he threw for 175 yards and 2 touchdowns.
Morton continued to back up Meredith over the next three seasons, getting a spot start here or there. 1967 actually saw him throw for almost 1,000 yards and 10 touchdowns while starting in three games.
After Don Meredith retired, Morton became the starter at QB for the Cowboys in 1969. And he had a terrific first year as the starter. He led the league in average yards per attempt and average yards per completion. He had a 10-2-1 record, throwing for 2,619 yards and 21 touchdowns.
After the 1970 season, Morton led the Cowboys to Super Bowl V, which was dropped to the Baltimore Colts 16-13.
The following season saw Tom Landry alternate quarterbacks between Morton and number 12, Roger Staubach, and eventually Staubach would wrest the starting position from Morton.
In all, Morton would play for Dallas over ten NFL seasons, throwing for 10,279 yards and 80 touchdowns in the regular season.