Nicholson and Cuthers were trying to steal electronics from Mr McMurdo's home, south of Helensville, when they killed him violently.
The pair had earlier visited the property to sell the victim methamphetamine, but the deal fell through, so they returned to seek revenge, the Crown said.
At the Court of Appeal, Nicholson's lawyer Chris Tennet argued three videoed interviews between his client and the police should not have been admitted as evidence at trial.
He also pointed to several alleged errors made by the High Court trial judge Justice Graham Lang.
But Justices Wild, Clifford and Dobson dismissed all appeal points.
They made similar rulings in response to Cuthers' lawyer Maria Pecotic, who also criticised the judge's summing up and directions to the jury.
However, the Crown's appeal to have Cuthers' minimum period of imprisonment extended was granted.
Crown prosecutor Kieran Raftery said the disparity between the sentences was "wrong in principle".
He said Cuthers had orchestrated the attack and although he did not inflict the fatal blows, the pair were "in it together".
The Court of Appeal agreed.
The two men will spend at least 17 years in prison before they are eligible for parole.
