As a rookie, he was a reserve playing behind Mel Renfro, until the fifth game when he was named the starter at free safety. Early in his first season, he forced a kickoff fumble that resulted in a touchdown. One of his 3 interceptions came against the Philadelphia Eagles, when he picked off a Norm Snead goal-line pass with two minutes left to secure a 21-19 win. Against the San Francisco 49ers, Larry Stephens blocked a field goal that Logan returned to the Cowboys 47-yard line, helping the Cowboys set up a last minute touchdown to end a 5-game losing streak. In the last game of the season against the New York Giants, he returned a blocked field goal by Cornell Green 60 yards for a key touchdown, helping his team win the game, complete the first non-losing season in franchise history and advance to the Playoff Bowl. In 1965, he was a key member of the special teams unit which blocked nine field goals (three times as many as other team in the NFL and Logan blocked two of those), 5 extra points and 1 punt, totaling 15 kicks blocked.