This paper aims to study the perspectives of sustainable development amid the COVID-19 pandemic and crisis in 2021, backed by financial risk management and corporate social responsibility. To achieve this goal, the authors use the methods of regression analysis, horizontal and trend analysis, and variation analysis. As a result, it is proven—for the first time—that in isolation, investments and corporate social responsibility do not contribute positively to sustainable development. In addition, the authors determine the absence of the outflow of investments from the world economy during crises. Based on this, a new approach to crisis management of sustainable development is developed—it is based on stimulating corporate social responsibility, for which the complex recommendations in the sphere of state management are offered. The theoretical significance of the conclusions made consists in specifying the essence of financial risk management of sustainable development, which has to be conducted with a strict connection to and based on corporate social responsibility. The practical significance of the developed new approach and offered recommendations on its practical implementation consists of strengthening the scientific and methodological provision of economic crisis management of COVID-19 and the maximization of its contribution to sustainable development to support the Decade of Action.