Currently, many countries are faced with the task of reducing the consumption of non-renewable energy resources, while at the same time ensuring the appropriate rates of economic growth. The main goal of this study is to assess the role played by overcoming obstacles on the way to technological upgrading to ensure the energy-saving economic growth of enterprises. The grouping of types of obstacles that stand in the way of energy-saving technological renewal of enterprises was performed, and indicators were constructed to determine the level of these obstacles. Tools and organizational mechanisms for overcoming obstacles on the way to energy-saving technological changes have been established. The methodological principles were tested using industrial enterprises in Ukraine. Among other things, it was found that with the increase in the overall level of obstacles that stand in the way of implementing projects of energy-saving (for natural gas) technological renewal, the share of those enterprises that during 2019–2021 had energy-saving economic growth decreases. At the same time, after the implementation of tools for overcoming obstacles that arise during the implementation of natural gas-saving technological changes, the share of companies that are characterized by energy-saving economic growth will increase: for enterprises that produce metal products—from 17 to 48%; for enterprises producing glass and glass products—from 19 to 52%; for enterprises that produce bricks and other construction materials from clay—from 20 to 47%. Therefore, reducing the level of obstacles during the implementation of gas-saving technological changes is an important factor in ensuring energy-saving economic growth of the studied enterprises.