Within the framework of institutional theory, this study explores how the proactiveness of focal (or buying) manufacturing firms, demonstrated through the adoption of various sustainability practices, influences the sustainability performance of suppliers. Additionally, it examines how the leadership capability of buying firms, particularly in terms of supply chain leadership, can play a crucial role in this link. Through empirical analysis of a sample taken from the fourth round of the High‐Performance Management (HPM) project, our study reveals compelling evidence indicating that buying firms, by adopting diverse sustainability practices, such as internal initiatives, monitoring efforts and collaborative approaches with suppliers, are able to create distinct institutional pressures. These pressures serve as a conduit for the diffusion of a shared set of sustainability goals, values and norms among suppliers, ultimately contributing to the development of sustainability competences and improving their overall sustainability performance. Furthermore, our findings suggest that when buying firms undertake a leading position, they can effectively translate isomorphism pressures into sustainability improvements on the supplier side. Overall, this study sheds light on important and understudied aspects of sustainability practices in buyer–supplier relationships and underscores the critical role that supply chain leadership can play in promoting sustainable practices across the entire supply chain.