There is acute paradox in petroleum-dependent economies as hydrocarbon rents are essential to fiscal stability, and they increase vulnerability to climate risks and distort sustainable development trajectories. To investigate this paradox, this paper develops the Governance Climate Renewables (GCR) model which aims to connect environmental, social, and governance (ESG) adoption, quality of governance, and climate responsibility in economies rich in resources. Based on quantitative and qualitative data, the paper combines a panel of 15 petroleum economies (2000-2023) and a deeper case study of Nigeria. Three composite measures are created, including: Petroleum Sector Sustainability Performance (PSSP), ESG Adoption Index (ESGAI) and Climate Accountability Score (CAS) that are validated by principal component analysis and cross-source triangulation. The econometric analysis, which is founded on fixed and random effects estimations show that strong ESG adoption correlates with a strong increase in governance and climate accountability, but that effects are dampened by institutional weaknesses and regulatory capture. The case study of Nigeria depicts these dynamics clearly which emphasizes the disjointed remediation programs under the Hydrocarbon Pollution Remediation Project (HYPREP), laxity in the implementation of disclosure policies and political inhibition of reform. These findings are placed in the wider context of debates on the resource curse, legitimacy theory, and energy transition governance and provide new empirical findings to ESG discussion. It is recommended to include ESG compliance in petroleum contracts, strengthen regulatory autonomy, invest more in renewables, and deal with institutional ties that hinder reform. Finally, the research illustrates that the effective institutionalization of the ESG can be a plausible way towards sustainable resource management and climate resilience in a fast-decarbonizing global economy.