Optimum soil moisture and high crop residue return (RR) can increase the active pool of soil organic carbon and nitrogen, thus modulating the magnitude of greenhouse gas (GHG) fluxes. To determine the effect of soil moisture on the threshold level of RR for the wheat production system, we analyzed the relationship between GHG fluxes and RR at four levels, namely 0, 5, 10, and 15 Mg ha−1 (R0, R5, R10, and R15) under two soil moisture content (80% FC and 100% FC) and three levels of nutrient management (NS0: no nutrient; NS1, NS2= 3x NS1). Nutrient input (N and P) in NS1 balanced the residue C/nutrient stoichiometry to achieve 30% stabilization of the residue C input in RR (R5). All RR treatments (cf. R0) were found to significantly reduce N2O emission in moderate soil moisture content (80% FC) by 22–56% across nutrient management due to enhanced soil C mineralization, microbial biomass carbon, and N immobilization. However, averaged across nutrient management, a linear increase in N2O emission was observed with increasing RR under 100% FC soil moisture. A significant decrease in CH4 emission by ca. 46% in most RR treatments was observed in 100% FC compared with the R0. The N2O emission was negatively correlated (p = <0.001) with nutrient stoichiometry. Partial least square (PLS) regression indicated that GHG emissions were more responsive (values > 0.8) to management variables (RR rate, nitrogen (N) input rate, soil moisture, and nutrient stoichiometry of C: N) and post-incubation soil properties (SMBC and NO3-N) in Alfisols. This study demonstrated that the mechanisms responsible for RR effects on soil N2O, CH4 fluxes, and carbon mineralization depend on soil moisture and nutrient management, shifting the nutrient stoichiometry of residue C: N: P.