They were also both required to work public holidays, but were not paid correct penal rates or given days off in lieu.
After a year and a half of employment, Mr Agustin's wage increased from $14 per hour to $17.50 per hour.
However, he said he was never paid at the increased rate.
Ms Agustin, who worked as a housekeeper, told the authority that for six months, she was paid almost nothing. Auckland Harbour Oaks' explanation was it was paying her wages into her husband's account, she said.
Authority member James Crichton said it was difficult to see how the company had been confused about how to pay Ms Agustin as she had a separate account to her husband.
He directed Auckland Harbour Oaks to attend investigation meetings with wage and time records, alongside any other documentation.
No documents were supplied, but Auckland Harbour Oaks maintained their pay regime was correct, and said if Mr or Ms Agustin had raised the matter with them earlier it would have been solved promptly.
However Mr Crichton said evidence he received showed Mr and Ms Agustin did this on a regular basis, and the problem remained unsolved.
The company was legally obliged to retain wage records and must have them available for inspection, Mr Crichton said.
"I am...satisfied that Auckland Harbour Oaks have failed absolutely to pay Mr and Ms Agustin correctly during the totality of the employment and accordingly I am satisfied that Mr and Ms Agustin are entitled to an order for arrears of wages."
Mr Crichton awarded Mr Agustin $38,832 and Ms Agustin $39,970 in outstanding wages and ordered the money be paid within 10 days of the decision being issued.
The chief operations manager for Oaks Hotels & Resorts, Mike Anderson, said "We were most distressed to learn of this situation, but uphold Oaks Hotels & Resorts were in no way responsible for the payment of wages to the Agustins, nor privy to the contractual arrangement they had with Auckland Harbour Oaks Limited.
"We are now investigating this matter and putting policies and procedures in place to ensure it does not occur again."
A spokesman for the couple said Mr and Ms Agustin were not confident they would be paid.