The latest application sparked 50 letters of support and only 11 from people objecting to the scheme.
Aldi supporters said Caird Avenue was an excellent site for the store. They added that extra competition could cut the cost of a weekly shop and also claimed that vibrant high streets "were a thing of the past".
Planning officers continued to argue that the supermarket should be built in the town centre but members approved the scheme.
The application was passed by 14 votes to 0, with one abstention.
A report to councillors acknowledged that previous reasons for refusal, including concerns about the quality of the landscaping, had been overcome.