A partygoer, who did not wish to be named, said he and another male rushed to the bottom of the staircase and attempted to heave against the descending tide to free the trapped.
"There were people fallen over up to my thighs and [for] everyone we picked up ... there was another underneath," he said.
"The third person I pulled up and out couldn't even stand up, she was on the verge of passing out from suffocation."
Police immediately cleared a path to the front door on arrival and that was when the witness saw Crestani on the floor.
"I just knew instantly we had to get her out of the way," he said.
He said some partygoers started to rush for the newly cleared space and the front door but other students held them back so Crestani could be carried free.
"The emergency services did an excellent job and thanks to them it didn't end any worse than it already did," he said.
"Another two, five, 10 minutes in there, who knows what could have happened to anyone else."
He recalled looking around the party at one point and seeing many "hysterical" people.
"There was also a lot of people trying their hardest to help, but there was only so much that could be done when you can only move inch by inch."
"Once people at the front of the crowd realised how bad the situation was, many people were trying their hardest to keep the crowd from the back from pushing any further forward."
Earlier he and another male took a place next to the hallway stairs in the house, known as The Manor.
"We had to squat down and push up and backwards to get some of the people away from the fallen," he said.
The pair also unsuccessfully tried to break down a bedroom door and create a second exit from the house.
Otago Coastal Area commander Inspector Marty Gray said the university's Campus Watch group made the first call to police five minutes before midnight on Saturday to report disorderly behaviour.
That call was followed by one from partygoers, asking for help to halt the event.
When police arrived, Crestani was carried out of the house. Police and others tried to revive her before St John arrived.
"When our officers arrived there was ... about 500 or 600 partygoers, a lot of them anxious, a lot of them trying to get out of the premises, a lot of them trying to get in the premises, a lot of disorganisation, a lot of uncertainty, a lot of anxiety," Gray said.
Two other people at the party were injured.
Partygoers' efforts to help the woman were "fantastic" and police did not meet any resistance at the scene, Gray said.
He told media it was too early to call the death an accident, and also too early to speculate whether charges would be laid.
The partygoer who had tried to help said he felt that a move to curb student drinking had played a part in the tragedy.
"If the council and uni are shutting down student bars and arranged areas for drinking, do they just think it's going to stop the drinking culture?"
"Less student bars means less places to drink under regulated control where people are paid to look out for intoxication and signs of bad situations and to defuse them."
"Less bars like these means more flat parties, it's that simple."