For a long time, fluctuations in international crude oil prices have been regarded as an important external risk source for macroeconomics. With the rise of the Chinese economy, China’s sensitivity to fluctuations in international crude oil prices is increasing, thus the impact of crude oil prices on China’s industrial output has attracted much attention. To better prevent the risk of oil price fluctuations and further stabilize industrial output, it is necessary to conduct a thorough analysis of the relationship between international crude oil prices and China’s industrial output. Starting from the fact that there is independence between international oil price fluctuations and changes in China’s industrial output, this article uses an SVAR model that combines external instrumental variables and symbolic constraints to decompose international oil price shocks and analyze industrial heterogeneity from July 1998 to September 2023, exploring the underlying mechanisms behind their independence. The research results indicate that, firstly, the impact directions of crude oil supply shocks, economic aggregate demand shocks, and specific demand shocks on changes in China’s industrial output are different. Among them, the impact of crude oil supply shocks on China’s industrial output dominated from 1998 to 2023. Secondly, the impact of crude oil supply shocks on industrial sectors with high R&D investment is minimal, while the impact on industrial sectors with low R&D investment is most significant. The industrial sector with high R&D investment shows the strongest recovery ability when dealing with economic aggregate demand shocks and specific demand shocks, followed by the industrial sector with moderate R&D investment. This conclusion confirms the view that the level of technological development can weaken the impact of international oil price fluctuations on changes in China’s industrial output. Thirdly, the sources of international oil price fluctuations, heterogeneity of China’s industrial sector, and temporal trends are the main reasons for the independence of the relationship between international oil price fluctuations and changes in China’s industrial output. Compared with previous studies, this article may have the following marginal contributions. Firstly, this article has identified the characteristic fact of independence between international crude oil price fluctuations and changes in China’s industrial output from the data, and the relationship between the two variables is not the simple positive or negative correlation that most scholars have empirically concluded before. Moreover, this article also deeply analyzes the reasons for the phenomenon based on the characteristic fact of independence. Secondly, this article adopts the cutting-edge SVAR recognition method that combines instrumental variables with symbolic constraints to more accurately identify various shocks from different sources in international oil price fluctuations. Thirdly, based on the exploration of the impact of international oil price fluctuations on industrial output heterogeneity, this article further studies the reasons for such heterogeneity and finds that technological innovation has a certain mitigating effect on the impact of international oil prices, and explores the economic stability role of technological innovation. Finally, based on the analysis of the entire article, this paper proposes suggestions to address international oil price fluctuations from multiple perspectives, including government, market entities, and economic researchers, including appropriately responding to international oil price fluctuations and easing market panic; strengthening the economic stability role of technological innovation, adhering to the practical logic of China’s new industrialization with Chinese characteristics, grasping the theoretical logic behind the special situation, and using scientific economic theories to guide practice, aiming to better promote the high-quality and efficient development of China’s economy.