Hennessey was ranked among the 10 best American players three times, his highest ranking being No. 4 in 1928. In both 1927 and 1928 he was the world No. 8 ranked player by
A Wallis Myers. Hennessey and
George Lott won the 1928 doubles title at the
U.S. Nationals, the same year that Hennessey lost two singles matches in the final Challenge Round of the
Davis Cup against
France. Hennessey reached the quarterfinals of the 1927 U.S. National championship and the quarterfinals at Wimbledon in both 1925 and 1928. A July 14, 1924
Time Magazine article called him
The Indianapolis Cyclone. He also won the 1920 singles title at the
Cincinnati Open. He reached the singles final there in 1919 and was the doubles champion there in 1917 (with Albrecht Kipp) and 1920 (with
Fritz Bastian). At the Western Tennis Championships he won the singles title in 1922 and was a finalist in 1924 and 1927. In doubles he won the title in 1924 and 1926 (both with
Alfred Chapin) and was a finalist in 1927 with
Emmett Paré. In 1934 he won the
Minnesota State Championships. Also in 1927, he was runner-up at the Illinois State championship, losing in a five-set final to
Bill Tilden. In 1984 Hennessey was one of the first four inductees into the USTA/Midwest Section Hall of Fame. There is an annual John F. Hennessey Open tournament in
Indianapolis for junior players. ==Grand Slam finals==