The 92-year-old from Bruce Rock became the first player to earn a Baggy Green while representing WA in the Sheffield Shield, when he was called up for Australia's match against India in Bombay in 1956.
His selection followed an excellent century during a trial match in Sydney, which Rutherford played despite suffering injuries in a car accident shortly before the game.
A stoic right-handed opener, Rutherford struck 30 and took a wicket bowling wrist spin during his sole appearance for Australia.
In total, he played 67 First Class games and tallied 3,367 runs at 31.76 with six centuries and 15 half-centuries. This included 2,200 runs at 37.93 in 33 Sheffield Shield matches.
Rutherford also travelled with the Australians during their 1956 tour of England, and gained the nickname Pythagoras while crossing the Pacific after explaining to teammate Keith Miller how to calculate the distance to the horizon by using Pythagoras' Theoram.
The nickname was befitting of Rutherford's profession as a mathematics and science teacher.
During his later years, Rutherford donned the Baggy Green as a regular guest of honour for the annual social cricket match played each January at Wedge Island near Lancelin.
WA Cricket Chief Executive Officer Christina Matthews said:
"John Rutherford played an enormous role in placing WA Cricket on the map, at a time when the national side was dominated by players from the Eastern States.
"He was a talkative and charismatic personality, and his passion for cricket was infectious.
"On behalf of everyone at WA Cricket and the State's cricketing community, we send our deepest condolences to the Rutherford family."