A clean and sustainable energy source, biogas is widely accessible worldwide. The caloric value of biogas is related to its methane content, and therefore removal of other gases is essential for reaping the benefits of this cleaner resource. In contrast to other classical techniques, membrane technology is relatively new yet extremely promising for methane enrichment. The methane enrichment performance of polymeric membranes is constrained, hence newer material combinations have been investigated to enhance membrane performance. In this study, blend membranes comprised of polyetherimide (PEI) and polyvinyl acetate (PVAc) in varying proportions were prepared by adopting the wet-phase inversion technique. The generated pure, and blend membranes were characterized for the morphological, thermal, and structural study. The interactions of PEI and PVAc in blend samples were verified by FTIR analysis. On the other hand, SEM investigation indicated that the membranes have an anisotropic porous structure with a dense skin layer at the top. Subsequently, a single glass transition temperature (Tg), as validated by DSC analysis, indicates that the blended polymers are miscible. Furthermore, membranes’ performance for gas separation was assessed regarding selectivity and permeance at feed pressures ranging from 2 to 6 bar. The permeation results showed that the CO2 permeance has increased by 40.47% with the addition of 4 wt % PVAc at 2 bar pressure. Furthermore, ideal selectivity improves as the blend ratio increases; nonetheless, the highest value for CO2/CH4 ideal selectivity was attained with a 2 wt % PVAc addition and at 2 bar pressure, which is approximately 26% greater than the pure PEI membrane. At 4 bar pressure, optimum CO2/N2 selectivity value of 22.50 was achieved. The findings indicate that PVAc is an excellent option for expanding the separation performance of blended polymeric membranes for biogas enrichment.