In November 2009 Ms Owen was told her lateness was not acceptable and if she did not improve her reliability, she would be fired.
She was issued a final warning for lateness in July 2011, which said: "...if there are any further infringements you will be given a week's notice terminating your employment".
After receiving the letter, Ms Owen said it was best if she resigned.
Mr Black said she could stay on until she found another job.
Ms Owen began job-hunting immediately and the following Tuesday she had a job interview, which Mr Black gave her time off to attend.
However, on the Monday before, on her way to work, Ms Owen's car broke down on the motorway and more than an hour later she texted Mr Black to say she would not be in, and she understood if she had "blown my chances".
Mr Black replied that she had "blown your job. Last pay tomorrow".
The authority said Ms Owen should have contacted her employer earlier but Mr Black had failed to adhere to paying her a week's pay as they had agreed or the two weeks pay that was stipulated in her contract.
A letter sent by Mr Black to Ms Owen after he had fired her also said that it was not acceptable for her to attend a job interview despite already allowing her the time off to go.
The authority said Mr Black "needed to do instead was to draw breath and have some form of investigation into what had occurred, as would be incumbent on any fair and reasonable employer".
It found Ms Owen was unjustifiably dismissed.
Mr Black was ordered to pay Ms Owen $9105.44 in payments made up of unpaid annual leave and two weeks' pay in lieu of notice, compensation, lost wages and costs.