The classical vertical shear instability (VSI) is a baroclinic instability that arises from height-dependent azimuthal velocities and is a leading candidate for driving anisotropic turbulence in discs with extended vertical modes. The classical VSI requires fast cooling times and radial temperature gradients, which are absent in an isothermal stratified (barotropic) setup. We investigate the dust-driven vertical shear instability in an isothermal, stratified shearing box, where the VSI is generated by drag forces acting on the gas due to dust rather than radial thermal stratification. We construct two-fluid (gas+dust) vertically stratified equilibria including dust diffusion and use these profiles to initialise 2D (radial-vertical) hydrodynamical simulations with FARGO3D. To separate dust-driven vertical shear instability (DVSI) from drag instabilities, we employ a dust-analogue model in which dust-induced drag on the gas is prescribed as a time-invariant and height-dependent acceleration, such that the underlying spatial distribution of the dust is assumed to be constant. The DVSI grows from regions of strongest vertical shear away from the midplane, exciting predominantly radially short, vertically extended disturbances (large k_x/k_z) and producing banded structures in the perturbed azimuthal and vertical velocities during the linear phase. In the nonlinear regime, the instability saturates via a Kelvin-Helmholtz-like parasitic instability that breaks the coherent vertical-shear modes into smaller-scale eddies, which balance the growth of the vertically extended modes, driving sustained vertical stirring. Dust-driven vertical shear can drive anisotropic turbulence and vertical mixing in an isothermal model without invoking global thermal gradients and could play an important role in the stratified streaming instability.