This study presents the development and characterization of polymer nanocomposites (PNCs) using polyvinyl alcohol (PVA) as a matrix, incorporating graphene (Gr) and natural quartz nanoparticles (NQNs) as nanofillers. The graphene content was fixed at 1 wt%, while the quartz content was varied at 3 wt%, 7 wt%, and 11 wt%. The NQNs were derived from natural quartz rocks, which were ground and milled to nanosize, emphasizing the utilization of natural materials. Comprehensive characterization was performed using X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), Fourier-transform infrared spectroscopy (FTIR), UV–visible spectroscopy (UV–Vis), and extensive electrical and dielectric measurements. SEM and EDS analyses revealed the nearly spherical shape of the NQNs, with sizes ranging from 25 to 88 nm and an average size of 61.2 ± 13.1 nm. XRD patterns indicated a decrease in crystallinity of the polymer matrix with increasing NQNs content, with the PVA/Gr-11 wt% NQNs showing nearly amorphous characteristics. FTIR spectra demonstrated the incorporation of NQNs within the PVA matrix, affecting the chemical bonding and reducing the intensity of characteristic peaks. UV–Vis spectra indicated a significant decrease in the optical bandgap with the addition of NQNs, suggesting enhanced electronic properties. The electrical conductivity measurements, at a frequency range of 50 Hz to 8 MHz and temperature range from 20 °C to 80 °C, showed that the incorporation of Gr, a two-dimensional (2D) material, and NQNs significantly enhanced the conductivity of the nanocomposites, with the optimal performance observed at 7 wt% NQNs. Dielectric measurements revealed that the PVA/Gr-7 wt% NQNs nanocomposite exhibited superior dielectric properties, with higher dielectric constant and lower dielectric loss compared to pure PVA. Nyquist plots indicated reduced bulk resistance and enhanced thermal stability for the PVA/Gr-7 wt% NQNs composite. Capacitance-frequency and conductance-frequency analyses of the fabricated capacitor confirmed this composite's superior performance for dielectric capacitors. The optimized PVA/Gr-7 wt% NQNs nanocomposite, leveraging the unique properties of natural quartz and 2D graphene, demonstrated significant improvements in electrical and dielectric properties, making it a promising candidate for advanced dielectric capacitors in energy storage applications. The study confirms the innovative use of natural and 2D materials to develop energy storage devices.