US Masters runner-up Spieth (67-72-69) joined Rumford (70-69-69) and overnight leader Chalmers (71-66-71) in front at five-under par as The Australian course bared its teeth in windy conditions.
Only eight players were under par after 54 holes in the tournament on a challenging day around the Jack Nicklaus-designed layout.
McIlroy dropped six shots off the pace after a horror round of five-over 76 and will have to to give it his all if he wants to defend his Australian Open crown in today's final round.
"The course is on a razor's edge as they are trying to create a golf course that's as unplayable as they can get it without it being so and it's right on that point," said Rumford.
"It's tough, I'm certainly not saying it's easy, you seem as though you are pedalling a million miles an hour going nowhere."
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