The question is impossible to answer with one thing; one could for instance say with some justification "the germ theory of disease" but then that goes back to the microscope — otherwise no one would ever have seen a germ — and that to the lens, and eyeglasses may be as important as germs, ft as germs, and so on. But I will give you my entry; to the amazement of my colleagues who think of me as the ultimate antireductionist, I will suggest a very reductionist idea: the quantum theory, and I include emphatically quantum field theory. The quantum theory forces a revision of our mode of thinking which is far more profound than Newtonian mechanics or the Copernican revolution or relativity. In a sense it absolutely forces us not to be reductionist if we are to keep our sanity, since it tells us that we are made up of anonymous identical quanta of various quantum fields, so that only the whole has any identity or integrity. Yet it also tells us that we really completely know the rules of the game which all these particles and quanta are playing, so that if we are clever enough we can understand everything about ourselves and our world. Note that I said understand, not predict — the latter is really in principle impossible, for reasons which have little to do with the famous Uncertainty Principle and a lot to do with exponential explosions of computations.
I would agree with whoever said "the scientific method" if I thought that was a single thing invented at some identifiable time, but I know too much history and see too much difference between different sociologies of fields.
Why has no one mentioned the printing press yet?
The other really profound discovery is the molecular basis of evolution, for which probably Oswald Avery deserves more credit than anyone. Evolution itself has, like the scientific method, much too complicated a history to class as a single invention.