Lower-tier suppliers' sustainability noncompliance and focal company's failure at meeting the expectations of the stakeholders to extend sustainability towards lower-tier suppliers carry multiple risks, tangible and intangible, to the focal company. It is expected that extending sustainability to suppliers at lower tiers through effective sustainability governance approaches (SGAs) can reduce these risks for focal companies. The existing literature lacks research on decision support tools using management science techniques to help decision makers choose the most suitable SGA/SGAs in a given situation and the risk management of SGAs in multi-tier supply chain. The present study develops a model-driven decision support system (DSS) using Bayesian network (BN) that can assist operations managers in selecting the most effective SGA/SGAs in multi-tier supply chain considering each situation. The developed DSS includes contingency factors and risk variables and their relationships which are identified through a systematic literature review and is applied to the multi-tier, sustainable supply chain of a multinational company operating in China to demonstrate its practical applicability. The DSS is then used in the risk management of the SGAs in multi-tier supply chain, which includes core steps such as identification of the contingency factors and risk variables, the prioritisation of the contingency factors and risk treatment. By Prioritising the basic contingency factors, ‘‘Focal company's sustainability knowledge’’ and ‘‘The specific nature of the materials sourced from lower-tier supplier’’, and ‘‘First-tier supplier's possession of internal resources'’ and ‘‘First-tier supplier's sustainability training’’ were identified as the two most important factors regarding their impact on the effectiveness of the direct and indirect approaches respectively. Detailed managerial implications related to the development and implementation of the DSS and the risk management process are also provided.