There was no dispute that death resulted from the ingestion of promethazine, the ingredient in Phenergan.
Milner's defence at trial had been that Mr Nisbet committed suicide.
Milner's argument on appeal was that the jury's verdict was unreasonable because the prosecution did not prove beyond reasonable doubt how it was possible for her to have administered the drug to her husband without his knowledge.
There was evidence that the crushed pills had a bitter taste, and that the amount of the drug required to poison Mr Nisbet may have meant he would have noticed the taste in his food.
Milner argued this meant the reasonable possibility of suicide was left open.
However, the judgement today said it was open to the jury to exclude the possibility of suicide on the evidence.
It was not necessary for the prosecution to prove exactly how Milner had administered the drug so that Mr Nisbet did not know about it, it said.
The mechanics of administering the drug was simply one factor for the jury to weigh up in the context of a strong circumstantial case.
There was also other circumstantial evidence that supported the jury's verdict, the ruling said.
Purchases of pills containing promethazine were able to be linked to Milner and a witness had seen her crushing pills.
She had also expressed a wish to kill Mr Nisbet and take advantage of his life insurance policy. Suicide notes given to the police by Milner contained errors and other features that matched samples of her writing.
The Court of Appeal also rejected an argument that Mr Nisbet's ill-health on the occasion of the attempted murder may have been caused by something other than ingesting promethazine.
There was sufficient medical and other circumstantial evidence on which the jury could have been satisfied that promethazine was ingested, the ruling said.
Last December a High Court jury found Milner guilty of murdering Mr Nisbet in 2009, and guilty of a second charge of attempting to kill him a fortnight earlier.
She made his death on May 4, 2009 look like suicide in the hope of cashing in a $250,000 life insurance policy.
And the mother-of-two nearly got away with it when police referred the Christchurch delivery driver's death as a suicide to a coroner.
But the Coroner Sue Johnson raised suspicions which prompted police to launch a homicide investigation.
In February, Justice David Gendall sentenced Milner to the statutory life imprisonment and imposed a minimum non-parole period of 17 years.
