Industry 4.0 (I4.0) technologies have demonstrated their potential to significantly drive innovation and enhance the performance of firms. However, I4.0 implementation is complex, requiring the application of diverse fields of knowledge and skill. Furthermore, although open innovation may contribute to the implementation of I4.0 technologies, the literature is still not clear about which open innovation practices best leverage the adoption of I4.0 technologies or how they might lead to improvements in product and process innovations, particularly when firms are facing turbulent environments. The present article aims to reduce this gap by investigating the relationships between open innovation, the adoption of I4.0 technologies, and product and process innovation performance, considering technological and market turbulence as moderating variables. As a research method, we carried out a quantitative survey of 246 industrial companies in Brazil. The results revealed that inbound open innovation flows can be used to support the adoption of I4.0 technologies, which in turn improves both process and product innovation performance. Our findings also indicate that in more technologically turbulent environments, the relationship between inbound open innovation and the adoption of I4.0 is stronger. Unexpectedly, the moderating role of market turbulence was not confirmed. The discussion arising from these findings addresses theoretical implications for the digitalisation of manufacturing, innovation management and contingency theory, as well as offering practical insights for managers and policymakers interested in performing I4.0-based innovation.