Using chairs and a milk crate, several people were able to pin the man to ground until authorities were able to arrive.
Witness Paul O'Shaughnessy said that he felt compelled to chase the man down.
"I don't know whether it's an instinct thing or what, but we was like, 'Right, we've just got to try and restrain this guy from doing anymore,'" O'Shaughnessy told reporters.
Authorities said the suspect stabbed a 21-year-old woman to death and injured another woman, 41. They added that the suspect suffered from mental illness.
But they fear his rampage could have been worse if brave bystanders hadn't stepped in.
"I want to acknowledge those people, those members of the public who got involved, they were brave and I can only use that word seriously," said Gavin Wood of the New South Wales Police Force. "They were significantly brave people."