I'm afraid you are not quite right.
Yes, Einstein did get a Nobel prize for work overturning a dominant theory.
Yes, Einsteins work on Relativity did overturn aspects of the then-dominant paradigm of Newtonian mechanics - indeed even Special Relativity destroyed the intuitive idea that there was an absolute reference for motion. There is no such thing as "at rest" except in a relative sense.
But the work Einstein got the Nobel for was not Relativity. It was for his earlier work on the Photoelectric effect which marked a move away from the then-dominant wave theory of light, back to a particulate theory (which was what Newton proposed !). This was one of the founding works of Quantum Mechanics - placing Einstein in the forefront of the two greatest achivements of 20th Century Physics.
So although your post contains a common and understandable error, the truth actually reinforces your point. Not only is Einstein chiefly remembered for his work overturning one dominant paradigm, he also recieved the Nobel prize for work overturning ANOTHER dominant paradigm. Two for the price of one :-)