Playing his college ball at Marquette, George Andrie played his entire 11-year career with the Dallas Cowboys. 

John Niland won the starting job at Left Guard for good in his second season in the NFL (1967) with the Dallas Cowboys, and would then go on to stake a claim as one of the elite Offensive Guards in the National Football League.  Niland would be named to the next six Pro Bowls and landed a pair of First Team All-Pros in the process (1971 & 1972).  The former Iowa Hawkeye would win a Super Bowl with the Cowboys in Super Bowl VI, and his upper-echelon blocking played a large part in that historic championship.

Ralph Neely was drafted by the Houston Oilers of the American Football League and the Baltimore Colts of the NFL, and he had secretly agreed to play for the Oilers (it was kept a secret so that he could play for the University of Oklahoma in the Gator Bowl). 

There are a lot of improbable runs to getting a Super Bowl Ring, but you might be hard-pressed to find a more unlikely one than Cornell Green.