Winter, who is transgender and identifies as a woman, must serve at least 19 years and four months' behind bars before being eligible for parole, while Te Amo was given a minimum period of 19 years.
The pair appealed against their convictions and life sentences, but the applications were dismissed by the Court of Appeal earlier this year.
In a judgment released today, the Supreme Court has also dismissed Winter's leave to appeal application, saying the arguments would in substance reprise those made before the Court of Appeal.
After taking Pairama, Winter and Te Amo tortured the 17-year-old over several hours, including burning her, before eventually giving her the chilling choice of how she wanted to die.
A noose was then fashioned out of some torn bedsheets and Pairama's lifeless body was wrapped in the sheets and plastic.
Her body was found, dumped in a rusty steel drum, by police in July 2018 when they searched an abandoned state house on Buckland Rd in Māngere.
The case involved Winter, 29, and Te Amo, 26, running what was described by the Court of Appeal as "cut-throat defences" as they blamed each other for murdering Pairama.
Crown solicitor Natalie Walker, who prosecuted Winter and Te Amo, said there appeared to be no reason for the "terrible loss of humanity".
Pairama's mother, Lena Hetaraka-Pairama, told the court in May 2020 she struggled to listen to what happened during her daughter's final hours.
"My hand shook from the hurtful, evil things I was hearing."
Wearing a T-shirt with her daughter's photo printed on it, she explained how she "still can't forgive myself" for not keeping Pairama safe.
"Every time I close my eyes, I see her smiling," she said of the teen who had been a student at Northland College in Kaikohe and loved kapa haka, singing and arts and crafts."
