MWCNTs/hectorite 3D hybrid filler was prepared from the 1:1 combination by weight of constituent MWCNTs (1D) and hectorite (2D) through simple dry grinding method. The resulting hybrid filler was subsequently utilized for the preparation of Ethylene-co-vinyl acetate (EVA)/MWCNTs/hectorite nanocomposites by solution intercalation method. Transmission electron microscopy and X-ray diffraction studies of the nanocomposites confirm homogeneous dispersion of the fillers in the polymer matrix. Mechanical, thermal and dielectric properties of neat EVA are significantly enhanced with increase in filler content. The improvement in tensile properties observed at 4 wt.% filler content are: 243% in tensile strength (1.78 MPa to 6.11 MPa), 105% in elongation at break (366% to 750%) and 426% in toughness (3.36 MPa to 17.67 MPa) without significant change (1.12 MPa to 1.31 MPa) in Young's modulus. Differential scanning calorimetry confirms significant increase in crystallinity, crystallisation temperature (Tc) and crystallite melting temperature (Tm) of the nanocomposites vis-a-vis neat EVA. Observed shift in Tc by more than 10 °C (~87 to ~98 °C) and Tm by more than 30 °C (~118 to ~151 °C) are really significant confirming the improved thermal stability of the nanocomposites. Maximum improvements in dielectric constant and AC conductivity observed at 5 wt.% hybrid filler content are ~25% and ~50% respectively. Superior mechanical properties of the nanocomposites combined with enhanced thermal stability and dielectric properties make it a prospective material for flexible dielectric applications. Properties attained can be attributed to improved polymer-filler interaction on account of homogeneous dispersion.