Intruders broke into the home of Penrith state MP Karen McKeown on the night of October 3 before taking her husband's car.
The vehicle was tracked the next afternoon to an underground car park, where approaching officers allege it began hurtling towards them.
Police shot at the car, injuring both occupants, men aged 26 and 34.
The younger man died in hospital of his injuries on Wednesday, police said.
Police cordoned off a suburban Sydney street at the scene of a shooting after which one man died. (Steven Markham/AAP PHOTOS)
Senior police say the officers had found the car in a locked garage.Â
"As they've opened that garage door, the vehicle has immediately accelerated towards them," Acting Assistant Commissioner Paul Dunstan told reporters on Friday.
Police were not physically injured.
The incident under a unit block at Wentworthville, in western Sydney, will be investigated by a critical incident team from the homicide squad.
It will also be subject to independent review.
Ms McKeown, who helped police find the alleged offenders using the in-car tracker, praised the authorities for their response.
"While I am shaken from the events, thankfully I am unharmed," she said in a statement.
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