The contractor–subcontractor relationship is evolving from a traditional structure to a collaborative and partnering arrangement, leading to subcontracting project success and relationship stability as dual goals. Subcontracting project success denotes a good performance assessed by cost, time, quality, and collaboration satisfaction, whereas relationship stability implies a tendency of long-term orientation toward the dyadic relationship. However, dependence asymmetry, which refers to the different dependence magnitude levels between general contractors and subcontractors, hinders such dual goals. This article collected 223 questionnaires from subcontractors to investigate how to reduce the negative effect of dependence asymmetry on subcontracting project success and relationship stability. Meanwhile, this article employed the fairness perception as the psychological mechanism to aggregate such negative effect and took an explicit contract as an efficient moderator to reduce it. Results confirm the context-sensitive nature of fairness perception, showing that distributive fairness perception and procedural fairness perception mediated the relationship between dependence asymmetry and two dependent variables (subcontracting project success and relationship stability), whereas the effect of interactional fairness perception was not significant. Moreover, an explicit contract weakens the negative impact of dependence asymmetry on distributive fairness perception and procedural fairness perception, while it does not regulate the impact of dependence asymmetry on interactional fairness perception. Theoretically, this article clarifies the necessity of emphasizing long-term relationship development between general contractors and subcontractors in construction. Furthermore, this article extends dependence asymmetry research in contractor–subcontractor collaboration by adding both the psychological lens of fairness perception and a restraining moderator of explicit contract. Practically, the findings help project managers to identify dual means of explicit contract and psychological perception to balance the degree of dependence asymmetry and prompt collaborative performance.