Rainfall–runoff phenomena are among the main processes within the hydrological cycle. In urban zones, the increases in imperviousness cause increased runoff, originating floods. It is fundamental to know the sensitivity of parameters in the modeling of an urban basin, which makes the calibration process more efficient by allowing one to focus only on the parameters for which the modeling results are sensitive. This research presents a formal sensitivity analysis of hydrological and hydraulic parameters—absolute–relative, relative–absolute, relative–relative sensitivity and R²—applied to an urban basin. The urban basin of Tuxtla Gutiérrez, Chiapas, in Mexico is an area prone to flooding caused by extreme precipitation events. The basin has little information in which the records (with the same time resolution) of precipitation and hydrometry match. The basin model representing an area of 355.07 km² was characterized in the Stormwater Management Model (SWMM). The sensitivity analysis was performed for eight hydrological parameters and one hydraulic for two precipitation events and their impact on the depths of the Sabinal River. Based on the analysis, the parameters derived from the analysis that stand out as sensitive are the Manning coefficient of impervious surface and the minimum infiltration speed with R² > 0.60. The results obtained demonstrate the importance of knowing the sensitivity of the parameters and their selection to perform an adequate calibration.