Public hospitals need supply chains that keep working under disruption, yet little is known about how digital governance relates to that outcome. This study examines a serial mediation model linking digital governance, digital capability, supply chain visibility, supply chain resilience, and sustainable performance (respondents’ perception). We surveyed 200 managers, pharmacists, procurement officers, logistics staff, financial controllers, IT specialists, and quality or risk officers from 50 Romanian public hospitals (four per hospital) in 2026. Paths were estimated by ordinary least squares on standardized composite scores, first as separate regressions and then as a recursive system, with hospital-clustered standard errors and cluster bootstrap intervals. In the recursive model, governance was related to capability (β = 0.76), capability to visibility (β = 0.64), visibility to resilience (β = 0.42), and resilience to sustainable performance (β = 0.58), all p < 0.001. The complete serial indirect association was 0.12 (95% CI [0.06, 0.18]), about 57% of the product of separate regressions, and it was smaller within hospitals (0.04), where governance varies little (ICC = 0.73). Convergent validity of visibility, resilience, and sustainable performance was weak. Under a cross-rater specification, the serial association was null, and the direct association of governance with sustainable performance changed sign, so the indirect result is not robust to the source of the ratings. The design is cross-sectional and relies on self-reports, so all results are statistical associations and do not establish causal mediation.