Artificial nitrogen oxide (NOx) emissions due to the combustion of fossil fuels constitute more than 75% of the total NOx emissions. Given the continuous reinforcement of NOx emission standards worldwide, the development of environmentally and economically friendly NOx reduction techniques has attracted much attention. This study investigates the selective non-catalytic reduction (SNCR) of NOx by methane, ammonia, and urea in the presence of sodium carbonate and methanol and the concomitant generation of N2O. In addition, the SNCR mechanism is explored using a chemical modeling software (CHEMKIN III). Under optimal conditions, NOx reduction efficiencies of 80–85%, 66–68%, and 32–34% are achieved for ammonia, urea, and methane, respectively. The N2O levels generated using methane (18–21 ppm) were significantly lower than those generated using urea and ammonia. Addition of sodium carbonate and methanol increased the NOx reduction efficiency by methane to ≥40% and 60%, respectively. For the former, the N2O level and reaction temperature further decreased to 2–3 ppm and 850–900 °C, respectively. The experimental results were well consistent with simulations, and the minor discrepancies were attributed to microscopic variables. Thus, our work provides essential guidelines for selecting the best available NOx control technology.