Officers were called to a home on Chris Court at Hillside, in Melbourne's northwest, over reports a man had been stabbed at 6.50am on Friday, police said.
The man, who is yet to be identified, was found with critical injuries on the front lawn and given CPR, but died at the scene.
Victoria Police allege a man armed with a weapon then approached officers.
"Police attempted to negotiate with the man before he advanced toward them," police said.
"Officers discharged a firearm and the male was struck to the lower body."
He is now in a critical but stable condition in hospital under police guard.
A woman who lives at the home and saw the incident unfold was also taken to hospital as a precaution.
Police are not looking for anyone else over the incident and believe those involved know one another, but have not revealed the connection between them.
Victoria Police's armed crime squad and professional standards command will investigate the shooting, which the force said was standard when officers discharged their firearms.
Homicide squad detectives are probing the fatal stabbing.
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