Previous research on sub-supplier management still lacks empirical results regarding the effect on sub-supplier performance. Previous findings established the relevance of a buyer-sub-supplier strategic consensus for sub-supplier management performance. Within this paper, we are testing the role of a strategic consensus at the level of sourced material/product group between buyer and sub-supplier regarding its influence on the link between sub-supplier management practices and sub-supplier performance (regarding on-time delivery and quality). The authors analyze empirical connected multi-tier data (matched-triplets) within a structural equation model applying Bayesian estimation of parameters. The analysis includes 17 different sub-supplier management practices. Our results strongly support a model of a mediated effect of sub-supplier management practices on sub-supplier performance through buyer-sub-supplier strategic consensus at the level of sourced material/product group. By reflecting our findings with the supply chain practice view (SCPV), we contribute to and extend the existing frameworks regarding the effects of practices in multi-tier supply chains.