On October 26, 1960, he was named Lineman of the Week by the Associated Press, after making his first field goal in an official game and contributing to a controversial last second upset of the University of Arkansas 10-7.
[2] Green contributed to the team finishing with a 10–0–1 record, with the lone blemish the 6-6 tie against an inferior LSU squad (the Tigers went 5-4-1 after winning 20 of 22 games in 1958 and 1959).
They also won the 1961 Sugar Bowl, defeating Rice University 14-6, the SEC championship and were recognized as national champions by the Football Writers Association of America.
The Redskins acquired Fred Dugan, placekicker John Aveni, defensive back Dave Whitsell and offensive end Jerry Daniels.
Green made a last second field goal in the season opener against the Pittsburgh Steelers, to earn the Cowboys first ever victory (27-24).