Eventually, a 17-year-old gang associate, Teina Pora, was arrested and convicted of the crime in 1994 after making inconsistent confessions.
But in 1996, DNA testing showed the semen inside Mrs Burdett belonged to serial rapist Malcolm Rewa, who was unknown at the time of Pora's trial but was convicted in 1998 of sexually assaulting 24 women.
Now the detective whose expert testimony convicted Rewa says he is convinced police got the wrong man for Mrs Burdett's murder.
"It's one that has stuck in the craw," Dave Henwood told the Weekend Herald this week. "There's no doubts in my mind."
Mr Henwood, a multi-award-winning criminal profiler who also helped catch South Auckland serial rapist Joseph Thompson, said that, in his opinion, Rewa committed the crime alone and Pora was innocent.
Rewa was tried twice for Mrs Burdett's rape and murder.
The jury at his first trial, which covered multiple sex attacks during the 1980s and 1990s, could not reach a verdict on the Burdett charges.
A second jury convicted Rewa of rape but could not decide on the murder charge.
Pora was convicted again in 2000 after a retrial was ordered.
Mr Henwood said the murder charge against Rewa failed only because Pora had already been wrongly convicted.
"You've got a joker [Rewa] who is not convicted of murdering Susan Burdett who did murder her," he said, "and the reason he is not convicted of it is because Pora is in the road."
His comments come soon after barrister Jonathan Krebs, a former Crown prosecutor, filed an application on Pora's behalf for the Royal Prerogative of Mercy, under which the Governor-General can order a new trial.
The Weekend Herald has also learned that an internationally renowned authority on suggestibility and false confessions, Gisli Gudjonsson, recently reviewed nine hours of videotaped interviews Pora gave police and visited him in prison.
Dr Gudjonsson, professor of forensic psychology at the Institute of Psychiatry, King's College, London, conducted pioneering research into how people might be induced to make "confessions" to crimes they hadn't committed.
His testimony is credited with leading to the overturning of the convictions of the Birmingham Six and Guildford Four - two groups of people wrongly accused of terror bombings in Britain.
Mr Krebs, who is convener of the New Zealand Law Society's criminal law committee, this week said he did not want to comment publicly.
He has previously said admissions Pora made were "false confessions" and he was confident his innocence could be proven.
The official police view is that up to four people were involved in Mrs Burdett's death.
This is based on Pora's original claim that two Mongrel Mob gang members he named were responsible.
But both men were cleared by alibi and DNA evidence.
The theory also clashes with the police case that convicted Rewa of the attacks on the 24 other women that he was a habitual lone serial rapist.
Mr Henwood, who retired five years ago as a detective but continues to work for the police as an unsworn officer, said he knew there were issues about Pora's confessions and about identification but he purposely avoided looking at them.
"My view stands solely on the behaviour of Malcolm Rewa and I drew my conclusions from that."
It wasn't plausible that a 40-year-old who was third in command of the Highway 61 gang and who was otherwise always alone when he attacked women would take a 16-year-old associate of arch-rival gang the Mongrel Mob along to watch him rape.
"That's the guts of it. I had a feeling this was all going to turn to custard somewhere down the track, and it should do because, you know, the truth has a tendency sometimes to ... come to the surface."
Lawyers acting for Pora have begun civil action in the High Court over the police's refusal to provide certain information from their files.
This is understood to include the extensive chart on Rewa's methods drawn up by Mr Henwood which was the centrepiece of Rewa's multiple convictions, and whether witnesses against Pora were paid.
A jailhouse informant and two other witnesses who were granted name suppression testified in the second trial to the collective effect that Pora and Rewa knew each other and that Pora had made admissions.
The Weekend Herald has been told evidence has emerged that "tends to impeach" some of this testimony.
Police this week would not say whether witnesses were paid.
"The matter has been before the High Court on two occasions," Detective Superintendent Andy Lovelock said.
"Teina Pora has been convicted on two occasions ... That's the case over."
Tim McKinnel, a private investigator working with Mr Krebs on Pora's behalf, said getting information from the police had been "like pulling teeth".
The former police detective said that more than two years on, "we still don't have some information we need, information we ought to have".
"In March 2010, we met police and asked to work collaboratively with them on a review of the case.
"They declined ... and said they would comply with the OIA [Official Information Act] and Privacy Act only," Mr McKinnel said.
Pora has been in jail for 19 years.
In 2010, the Parole Board said that his continued denial and "his lack of motivation" meant he could not attend a violence prevention unit which could aid in a possible early release.
The board noted there were "complications about his conviction".
"To put the matter in context, it is enough to say that evidence is being accumulated because of serious concerns by serious people that there may have been an injustice."
