[1] In college, Nagler played on the UCLA Bruins men's basketball team for Hall of Fame coach John Wooden in 1958 and 1959.

Nagler was a three-time Intercollegiate Tennis Association (ITA) First-Team All-American (1960–62), and was the only player to ever win three Pac-10 men's singles titles (1960–62).

[6] At 17 Nagler began attending the University of California, Los Angeles, (UCLA) at the urging of his best friend, tennis player Allen Fox, whom he had known since he was 13 years old.

[11][3] Nagler described his relationship with Fox, who was UCLA's top player, as "We were bitter rivals and close friends.

"[8] In turn, Fox recounted he "was psyched out by his speed on the court, his physical abilities, and his ferocious competitiveness.

"[8][13] Nagler and Fox won the doubles title at Ojai in 1961, defeating Bill Hoogs and Jim McManus.

[10] Nagler won the 1962 Detroit Tennis Club invitational with doubles partner, and future Hall of Famer, Arthur Ashe, defeating Andy Lloyd and Don Russell.

[21] Nagler and Ashe also won the 1962 Pennsylvania Lawn Tennis Championships, defeating Bill Bond and Ramsey Earnhart in straight sets.

[24] He won the Middle Atlantic invitation grass courts championship, defeating Frank Froehling.

He also played singles in the 1964 Wimbledon Championships, losing in the first round to # 4 seed and future Hall of Famer Rafael Osuna.

[25][26] At the 1977 Maccabiah Games in Israel, Nagler and Steve Krulevitz were partners and won gold medals in doubles for the United States.

[10] He has represented, among others, tennis players Arthur Ashe and Tom Okker, and actor Sylvester Stallone.