The right-handed opener made 30 and took a wicket in the second innings, dismissing Vijay Manjrekar at the Brabourne Stadium in the drawn match.
Rutherford, who hailed from Bruce Rock, a small country town 243km east of Perth, played 67 first-class matches between 1952-53 and 1960-61 scoring 3367 runs at 31.76 with six centuries and 15 half-centuries.
“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,” Matthews said.
“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.”