Uncertainty quantification (UQ) is becoming an essential attribute for development of computational tools in gas turbine combustion systems. Prediction of emissions with a variety of gaseous fuels and uncertain conditions requires probabilistic modeling tools, especially at part load conditions. The aim of this paper was to develop a computationally efficient tool to integrate uncertainty, sensitivity, and reliability analyses of CO and NOx emissions for a practical swirl-stabilized premixed burner. Sampling-based method (SBM), nonintrusive polynomial chaos expansion (NIPCE) based on point collocation method (PCM), Sobol sensitivity indices, and first-order reliability method (FORM) approaches are integrated with a chemical reactor network (CRN) model to develop a UQ-enabled emissions prediction tool. The CRN model consisting of a series of perfectly stirred reactors (PSRs) to model CO and NOx is constructed in Cantera. Surrogate models are developed using NIPCE-PCM approach and compared with the results of CRN model. The surrogate models are then used to perform global sensitivity and reliability analyses. The results show that the surrogate models substantially reduce the required computational costs by 2 to 3 orders of magnitude in comparison with the SBM to calculate sensitivity indices, importance factors and perform reliability analysis. Moreover, the results obtained by the NIPCE-PCM approach are more accurate in comparison with the SBM. Therefore, the developed UQ-enabled emissions prediction tool based on CRN and NIPCE-PCM approaches can be used for practical combustion systems as a reliable and computationally efficient framework to conduct probabilistic modeling of emissions.