Corporate governance reflects the managerial principles adopted by firms and influences various performance parameters. Companies with robust corporate governance mechanisms tend to establish a high level of trust with their stakeholders. This paper examines corporate governance parameters alongside financial indicators to provide insights into company performance. The primary objective of the study is to develop a robust decision support system for analyzing decision-making models based on corporate governance and financial performance indicators. In this context, a hybrid method combining single-valued triangular neutrosophic (SVTN), step-wise weight assessment ratio analysis (SWARA), and reference-based normalization alternative ranking (RBNAR) is proposed. The weights of the criteria affecting firm performance are determined using the SVTN-SWARA method, while firm performance levels based on these weights are obtained through the RBNAR approach. The SVTN-SWARA-RBNAR hybrid method is applied to thirty-two companies listed in the Borsa Istanbul Corporate Governance Index over a three-year period (2021–2023). The core finding indicates that the SVTN-SWARA-RBNAR method provides accurate and consistent company rankings, with AKSA achieving the highest performance. Among the financial criteria, net profit margin is identified as the most critical indicator. Within corporate governance parameters, the board of directors’ score emerges as the most significant factor. The robustness of the proposed method is further reinforced through sensitivity analyses.