However, it was in the late 1930s that Fritz Zwicky inferred the presence of dark matter based on his observations of Coma galaxy cluster using the virial theorem. Herein lies my confusion. Why does the scientific community and people, in general, give credits to Vera Rubin instead of Zwicky for inferring/observing the evidence for dark matter? Or, is the recognition given because she independently strengthened Zwicky's observation thereby confirming the existence of dark matter?
You have a clear view of the history, and it wasn't an independent confirmation, it was simply the best evidence. Whenever one talks about the discovery of dark matter, one should start with Zwicky, and move to Rubin. One might do something similar with the Big Bang, starting with Hubble, and moving to Penzias and Wilson. Normally we give credit both to the initial discovery, and to the confirmation, but it is the most conclusive evidence that generally gets associated the largest credit. After all, it was Edgar Allan Poe who first described the Big Bang model, but he gets no astronomical credit because he provided no evidence. Zwicky certainly did better than that, so does deserve (and should receive) much credit, but there were still many doubters in his day, much as with Hubble and the Big Bang. Perhaps Zwicky's role contributed to the reason that Rubin never received the Nobel prize, I hope it wasn't simply the unspeakable reason, but of course it's too late now for both of them.