This research examines the impact of oil prices, economic globalization, and inflation on the economic output in oil-producing countries in Latin America. We employ advanced time series techniques to achieve precision in findings and reliability of policy inferences. We use cointegration techniques with and without structural breaks because oil prices are highly volatile, and the economies analyzed are unstable in the face of political and social changes. Additionally, we performed a sensitivity analysis using standard quantile and the newly developed quantile-on-quantile regressions to measure the impacts of the covariates on real per capita output. Finally, we use causality Fourier techniques to identify the direction of causal relationships between the series. We found that the oil price, economic globalization, inflation, and output have a long-term equilibrium relationship in the presence of structural breaks. Likewise, quantile models show that the impacts of inflation, economic globalization, and oil prices on economic output are extensively non-linear across the quantile distribution. We found a negative connection between inflation and economic output in the surveyed territories. We propose that those responsible for energy policy in the countries studied should rethink crude oil policies to maximize the benefits of oil exploitation under stagnant globalization and growing inflation.