Construction capital expenditure is a strategic fiscal instrument for delivering public infrastructure, but its contribution to construction quality is not determined solely by the size of the allocated budget. In public construction projects, fiscal allocation is converted into project outcomes through cost estimation, procurement mechanisms, contractor bidding behaviour, bid price reasonableness, contractor capability, risk management, contract functions, and quality control. This study systematically reviews the relationship between construction capital expenditure, bid price, and construction quality in public construction projects. A PRISMA-based Systematic Literature Review was conducted by synthesizing 57 selected scholarly sources consisting of 39 core synthesis sources, 11 included-with-caution sources, and 7 supporting references. The novelty of this study lies in the development of a fiscal–procurement–quality framework that positions bid price as a conceptual mediating mechanism between construction capital expenditure and construction quality. By integrating Public Fiscal Theory, the Cost-Based Pricing Perspective, and the Resource-Based View, this review explains how public fiscal allocation is translated into contractor implementation capacity and construction quality through procurement mechanisms. The findings identify five dominant themes: construction capital expenditure and budget governance, bid price formation and public procurement, contractor capability and performance, construction quality and quality risk, and digital cost–quality governance. Practically, the study emphasizes value-based procurement, rational bid price evaluation, contractor capability assessment, risk-based project control, contract-function governance, and digital transparency to improve construction quality in public construction projects.