They face deportation back to Fiji when they are released after serving half of that period.
"It is difficult to imagine a more vulnerable victim in our society," Judge Emma Aitken said in sentencing the duo.
"This was a very gross and serious breach of trust."
Judge Aitken said there was no truth to the couple's claims they stole the money out of desperation to survive.
"I reject that explanation - $37,000 over three months has nothing to do with need and everything to do with greed."
New Zealand Aged Care Association chief executive Martin Taylor said it was extremely rare for such a crime to be committed by an aged care worker, who undergo criminal history and reference checks before they are employed.
"While both of those are done, when you have 35,000 caregivers (in New Zealand) it's just normal human nature that some of them are going to be bad, there's nothing you can do about that," Mr Taylor said.
"While we do the best we can and we succeed most of the time, occasionally someone (who goes on to commit a crime) gets through and this is an example that it's the exception that proves just how robust the systems are."
Mr Taylor said the Mercy Parklands Retirement Home was "one of the most respected operators in Auckland with a long history of providing great care over many years".
The home's chief executive Ann Coughlan would not comment.
Devi and Chand used the stolen money to pay for immigration and study fees, including a catering course for Chand.
Fears were raised when solicitors who held power of attorney over the elderly woman's accounts noticed large sums of money had been withdrawn.
Police investigated and tracked down the ATMs being used.
CCTV footage from the machines identified Devi and Chand and the pair were arrested.
They pleaded guilty last month to 33 charges of unlawfully using the elderly woman's bank card to gain a financial advantage.
Defence lawyer Baden Meyer, who requested they be sentenced to home detention with the pastor of their church at Papatoetoe, said their offending snowballed.
"They did it once, that was wrong. They didn't get caught so they did it again."
Both Devi and Chand were remorseful and wanted to pay the money back, he said.
But Judge Aitkin said neither had the capacity to repay the elderly woman and would likely be deported as soon as they were freed from jail.
She described their offending as "relentless", including periods where thousands of dollars would be withdrawn on consecutive days.
