Police have charged a man with assault following the death.
Detective Inspector Kevin Hooper said it was understood the man was assaulted in the park, which is known to be frequented by homeless people, between 6.30pm and 10.30pm.
A source close to the incident, who the Herald has agreed not to name, said the victim's friend tried to seek help following the attack.
The friend, who is also understood to be homeless, ran to the hospital's emergency department about 10.15pm, the source said.
Police were alerted almost immediately but an ambulance was not called for more than 35 minutes, the source said.
"The man's companion made a huge fuss, pleading for help and asked to be taken to the dying man," the source said.
"The companion's concerns were so grave police were called to investigate. They claimed not to be able to find the dying man and cancelled the ambulance and dismissed the man's claims.
"[The friend] then returned to the park on foot and, with help from another man, carried the dying man to the hospital, where he died shortly after arriving."
It was "deplorable" his cries for help were ignored, the source said.
An Auckland District Health Board spokeswoman confirmed a man came to ED to report his injured friend.
"ED staff reacted in accordance with protocols and immediately called police and ambulance to respond to the man's concerns," she said.
A St John spokesman said an ambulance was called at 10.52pm and dispatched to Outhwaite Park where it was reported a 45-year-old man was injured.
"The ambulance was stood down by police at 11.12pm."
It is not known why the ambulance was stood down.
Mr Hooper said police were called by hospital staff at 10.16pm, but the man's directions were vague.
"The informant left the emergency department after giving unclear information about the location of his friend. He later carried his friend to Auckland Hospital where he was pronounced dead.
"The investigation ... is ongoing and, until further inquiries are carried out into exact timings of calls between agencies and emergency services, police are unable to be specific about such interactions."
The Independent Police Conduct Authority had not received a complaint last night.
The victim's name is yet to be released while police locate his next of kin.
Auckland City Missioner Diane Robinson said it was a sad situation that highlighted the risks facing the homeless.
"It's sad that something happened and a person called for help and he was not heard. Homeless people are a very vulnerable group. They are out in anti-social hours and are more likely to be attacked or to be hurt or to come to some sort of harm and that is the huge issue with people who are sleeping rough."
Timeline
6.30pm - about 10.30pm: Homeless man assaulted.
10.15pm: Victim's friend runs to Auckland City Hospital for help.
10.16pm: Police called.
10.52pm: Ambulance called.
About 11pm: Victim carried to hospital by friend.
11.12pm: Police stand ambulance down.
11.19pm: Victim dies.
