In a competition for the theory with the most impact on economics and public awareness of economics over the last twenty years, the theory of central bank independence would be a strong contender. The idea is that governments should not set interest rates on a day-to-day basis, but rather tell someone else what inflation rate they want and then let that someone else set interest rates to obtain an inflation rate close to the target. Inflation can be controlled by interest rates (since with high interest rates, economic activity slows down because borrowing is expensive, and so does inflation), and the central bank (the government's bank) is the organisation to control inflation because they have access to such large amounts of money that they can influence interest rates unlike anyone else.
There are many design considerations for the central bank. How often should it report back to the government? What role should the government have? Is the arrangement democratic? Should the central bank only think about inflation or worry about the effect of its actions on output too? What sort of person should be head of a central bank?
The theory's importance was boosted by a number of factors - it followed a period of very high global inflation and a subsequent slump, it coincided and anticipated increasing concern with institutional arrangements in economic affairs, it is comparatively easy for policymakers to understand and implement the recommendations, and its subject is considered important in neo-liberal economics' worldview.
The modern theory received its present impetus in a paper from 1985 entitled "The optimal degree of commitment to an intermediate monetary target", which by virtue of its topic is arguably the theoretical paper with the most impact since its publication. It produces theoretical results in most of the major pure economic aspects of optimal design, it uses mathematical models without the reader feeling that the theory would collapse entirely if the assumptions are varied, and it has a high ratio of clearly derived results to discussion. If the paper's extreme influence was inflated by circumstance, it took full advantage of the opportunity.