I have found a basic mistake in one of the published paper in a top tier Applied Mathematics journal. I have told my research supervisor about it and he also agrees with me. I found the issue when I was working on one open problem mentioned in the paper. Please suggest what to do.
That depends on the consequences of the mistake. Does it invalidate the main conclusions of the article or is it only a side issue? If the former, you can write up what the consequences are and present the new results as an article an submit it. If it is only a side issue, you can mention it in a footnote when writing up your results for the open problem.
In the former case, keep the tone professional: don't use any adjectives to describe the mistake and certainly not when refering to the authors, i.e. it is a mistake not a basic mistake. Focus on the point you want to make, and let the strength of the argument speak for itself.
Although not an answer to your question, there is also this article that I found to be a very interesting read on addressing mistakes discovered in previously published papers.