Most commercial software used to simulate the injection molding process of semi-crystalline thermoplastic polymers do not explicitly take into account the polymer crystallization, which could lead to errors in the estimations of filling as well as warpage and shrinkage. This is mainly due to the common complexity of the models used to describe crystallization and the challenging respective model parameter identification under injection molding conditions. To close this gap, in this work we use a simple thermo-mechanical crystallization model to describe the flow-induced and quiescent crystallization of an unreinforced semi-crystalline thermoplastic material during injection molding. The crystallization model is implemented in the commercial software Autodesk Moldflow Insight 2021 using the Solver API feature alongside crystallization-dependent viscosity, PVT and solidification models. The model parameters were identified using a calibration workflow that employs surrogate models representing the simulated pressure results to perform a multi-objective optimization. The filling predictions as well as the calculated pressure fields are presented using the calibrated model parameters in comparison to those measured during the actual injection molding of a polyoxymethylene (POM) part using different process conditions. The results show major improvements in the estimations of the time-depending pressure field as well as the level of filling of the produced parts.