In tracked and highly stratified educational systems, where educational reproduction is particularly strong, the chances of students to achieve more education than their parents did are truncated. Little is known, however, what may help students raised in lower-educated families to become upwardly mobile at the transition to upper-secondary education. In tracked educational systems, this transition is decisive for ultimate educational attainment across the life course. The study addresses this research gap by examining whether quality of social relationships (i.e., social capital) among students, parents, and teachers matters for student and teacher assessment of students' agentic capabilities (i.e., work habits) at age 15. If so, the question is whether these assessments help students become enrolled in high-status upper-secondary school tracks at age 18, thus achieving educational upward mobility. The analyses are based on 401 students from two cohorts in the German- and French-speaking parts of Switzerland, interviewed at the ages of 15 (T1) and 18 (T2) (60.35% females, Mage 15 = 15.2, SDage 15 = 0.2; 58.35% older cohort), including data collected by questionnaire from primary caregivers and teachers at student age of 15. The students come from families where highest parental education attainment is below the high-status academic or vocational baccalaureate in upper-secondary education. They may thus experience the opportunity to gain access to these high-status tracks at the transition to upper-secondary education. A structural equation model reveals the role of student assessment of their agentic capabilities and teacher assessment of these competencies in mediating the relation of social capital accrued at home and at school to educational upward mobility. This novel evidence on mechanisms of social advancement may be prone to inform interventions helping students from less-educated families to succeed in tracked and stratified educational systems.