This paper reports a detailed analytical and numerical investigation on free convection flow of viscous fluid through a porous medium due to the combined effects of thermal and mass diffusion. Effect of temperature-dependent viscosity and thermal conductivity is investigated in the presence of first-order chemical reaction. The non-Darcy model is applied to define the porous matrix. The effects of viscous and Darcy dissipations are taken into account. The governing equations of continuity, momentum, energy, and concentration which are coupled nonlinear ordinary differential equations are solved analytically using regular perturbation method and numerically using Runge-Kutta shooting method. Brinkman number and variable thermal conductivity parameters are used as perturbation parameters. The velocity, temperature, and concentration distributions are discussed numerically and plotted in graphs. The effects of variable viscosity parameter, variable thermal conductivity parameter, thermal Grashof number, mass Grashof number, Brinkman number, wall temperature ratio, and first-order chemical reaction parameter on the flow fields are explored. The effects of physical parameters such as skin friction and Nusselt number at both the plates are derived and discussed, and the numerical values for various values of physical parameters are presented in tables. The solutions obtained using Runge-Kutta shooting method and using perturbation method are compared and the solutions agree very well in the absence of perturbation parameter.