Background: Glioma stem cells (GSCs) have self-renewal and tumor-initiating capacities involved in drug resistance and immune evasion mechanisms in glioblastoma (GBM). Methods: Core-GSCs (c-GSCs) were identified by selecting cells co-expressing high levels of embryonic stem cell (ESC) markers from a single-cell RNA-seq patient-derived GBM dataset (n = 28). Induced c-GSCs (ic-GSCs) were generated by reprogramming GBM-derived cells (GBM-DCs) using induced pluripotent stem cell (iPSC) technology. The characterization of ic-GSCs and GBM-DCs was conducted by immunostaining, transcriptomic, and DNA methylation (DNAm) analysis. Results: We identified a GSC population (4.22% ± 0.59) exhibiting concurrent high expression of ESC markers and downregulation of immune-associated pathways, named c-GSCs. In vitro ic-GSCs presented high expression of ESC markers and downregulation of antigen presentation HLA proteins. Transcriptomic analysis revealed a strong agreement of enriched biological pathways between tumor c-GSCs and in vitro ic-GSCs (κ = 0.71). Integration of our epigenomic profiling with 833 functional ENCODE epigenetic maps identifies increased DNA methylation on HLA genes’ regulatory regions associated with polycomb repressive marks in a stem-like phenotype. Conclusions: This study unravels glioblastoma immune-evasive mechanisms involving a c-GSC population. In addition, it provides a cellular model with paired gene expression, and DNA methylation maps to explore potential therapeutic complements for GBM immunotherapy.