Three-dimensional printed plastic products developed through fused deposition modeling (FDM) endure long-term loading in most of the applications. The tensile creep behavior of such products is one of the imperative benchmarks to ensure dimensional stability under cyclic and dynamic loads. This research dealt with the optimization of the tensile creep behavior of 3D printed parts produced through fused deposition modeling (FDM) using polylactic acid (PLA) material. The geometry of creep test specimens follows the American Society for Testing and Materials (ASTM D2990) standards. Three-dimensional printing is performed on an open-source MakerBot desktop 3D printer. The Response Surface Methodology (RSM) is employed to predict the creep rate and rupture time by undertaking the layer height, infill percentage, and infill pattern type (linear, hexagonal, and diamond) as input process parameters. A total of 39 experimental runs were planned by means of a categorical central composite design. The analysis of variance (ANOVA) results revealed that the most influencing factors for creep rate were layer height, infill percentage, and infill patterns, whereas, for rupture time, infill pattern was found significant. The optimized levels obtained for both responses for hexagonal pattern were 0.1 mm layer height and 100% infill percentage. Some verification tests were performed to evaluate the effectiveness of the adopted RSM technique. The implemented research is believed to be a comprehensive guide for the additive manufacturing users to determine the optimum process parameters of FDM which influence the product creep rate and rupture time.