Heath was the inaugural winner of the Australian Championships in 1905 and won again five years later in 1910.

He won the Australian Open doubles in 1906 with Tony Wilding and in 1911 with Randolph Lycett.

Heath finished runner-up at the Australian Open doubles in 1910 with JL Odea and 1914 with Pat O’Hara Wood.

He played two Davis Cup ties for Australia in 1912, compiling a 1-2 record in singles.