In today’s complex labor market, social sciences graduates encounter various challenges and negative experiences in their current jobs and job transitions, which may threaten the sustainability of their careers. Possessing 21st-century skills is considered important in supporting their career sustainability. Employing a cross-sectional survey design, this study investigated which 21st-century skills help social sciences graduates build a sustainable career after their graduation. The sample consisted of 129 early-career social sciences graduates. We utilized both a variable-centered (path analysis) and a person-centered (latent profile) approach to data analysis. The path-analysis results showed that collaboration, creativity, and problem solving, but not communication and critical thinking, related to career sustainability. The results also revealed a suppressor effect of problem solving on the positive relationships between creativity and health-related problems, suggesting that problem solving may prevent creative individuals from developing health-related issues. Furthermore, latent-profile analysis demonstrated two profiles: sustainable and non-sustainable careers. While both profiles exhibited similar productivity levels, individuals from the non-sustainable profile reported lower happiness and higher health problems. Partly corroborating the path-analysis results, graduates with sustainable careers differed in communication and collaboration skills. This study enhances the understanding of 21st-century skills’ role in career sustainability and validates the model of sustainable careers.