Skeletal reaction models are derived for a four-component gasoline surrogate model via an instantaneous local sensitivity analysis technique. The sensitivities of the species mass fractions and the temperature with respect to the reaction rates are estimated by a reduced-order modeling (ROM) methodology. Termed "implicit time-dependent basis CUR (implicit TDB-CUR)," this methodology is based on the CUR matrix decomposition and incorporates implicit time integration for evolving the bases. The estimated sensitivities are subsequently analyzed to develop skeletal reaction models with a fully automated procedure. The 1389-species gasoline surrogate model developed at Lawrence Livermore National Laboratory (LLNL) is selected as the detailed kinetics model. The skeletal reduction procedure is applied to this model in a zero-dimensional constant-pressure reactor over a wide range of initial conditions. The performances of the resulting skeletal models are appraised by comparison against the results via the LLNL detailed model, and also predictions via other skeletal models. Two new skeletal models are developed consisting of 679 and 494 species, respectively. The first is an alternative to an existing model with the same number of species. The predictions with this model reproduces the detailed models vital flame results with less than 1% errors. The errors via the second model are less than 10%.