Background: Sleep disorders are highly prevalent among healthcare workers (HCWs) globally, with occupational stress (OS) being a major underlying cause. Psychological capital (PsyCap) may serve as a protective resource, yet its combined relationship with OS and sleep quality remains underexplored. Objectives: We aimed to identify distinct OS-PsyCap profiles among HCWs, examine their associations with sleep quality, and investigate the mediating and moderating roles of PsyCap. Methods: A cross-sectional study was conducted among 1046 HCWs in Shanghai in December 2024. The Job Content Questionnaire, Psychological Capital Questionnaire, and Pittsburgh Sleep Quality Index were used to measure OS, PsyCap, and sleep quality, respectively. Latent profile analysis (LPA) was conducted to identify OS–PsyCap subgroups. Generalized linear models (GLM) and moderation and mediation analyses were performed to examine associations and to elucidate the role of PsyCap. Results: HCWs were divided into two distinct profiles: Class 1 (low OS and high PsyCap, 45.2%) and Class 2 (high OS and low PsyCap, 54.8%). HCWs in Class 2 had significantly poorer self-rated health and more sleep disturbances. Higher job demands and organizational support were associated with worse sleep outcomes, while higher autonomy and higher PsyCap were protective. In mediation and moderation analyses, PsyCap mediated 16.4–37.8% of OS–sleep relationships but also amplified OS effects on certain sleep outcomes under high stress. Conclusions: High OS with low PsyCap significantly increased sleep disorder risk among HCWs. PsyCap exhibited dual mechanisms, mediating stress effects while exacerbating sleep issues in high-stress contexts. Targeted interventions should address these HCWs in distinct profiles and pathways.