[4] Attending the school on scholarship, Greenberg was captain of the Northwestern University tennis team and became that school's first Big Ten Conference singles champion when he won the title in 1940.

Greenberg's three doubles titles still rank first all-time in Big Ten history.

He led the Northwestern Wildcats to the Big Ten team championships in 1940 and 1942.

[11] In 1943 at the Cincinnati Open, Greenberg reached the singles and doubles finals but lost the singles final to future International Tennis Hall of Fame inductee Bill Talbert.

Greenberg's sister Toby played in the Maccabiah Games in Israel.