The Pakenham Upper shooting had its origins about 3pm on Wednesday, when police were called to Endeavour Hills to investigate a serious assault.
Later, a yellow Hyundai believed to be connected to the assault was spotted in Narre Warren.
The vehicle was then sighted several times in surrounding suburbs before police gave chase about 9pm and deployed stop sticks.
Police said the man got out of the car with knives and allegedly threatened officers before he was shot. His condition is unknown.
The second police shooting incident began when officers were called to Franklyn Street, in Oakleigh East, about 11pm after reports that six men armed with knives and a long-arm firearm had forced their way into a home and assaulted two men in their 20s.
The offenders then got into two vehicles and drove away.
Officers en route to the incident noticed one of the cars, a silver Holden Commodore, leaving Franklyn Street and heading along Keith Street, police said.
The car was pursued and intercepted on North Road, Clayton, near Beleura Grove, where officers arrested a male passenger in the front seat without incident.
The driver refused get out and “was seen attempting to access under his seat”, police said in a statement.
An officer fired, but police provided no further information other than no one was injured and the target got away.
The two occupants of the house were taken to hospital with non-life-threatening injuries.
Zach is a reporter at The Age. Got a story? Email me at firstname.lastname@example.org