A novel approach is introduced to study a lid-driven, skewed cavity flow via utilizing a non-orthogonal, body-fitted coordinate system, employing the primitive variables. The Navier-Stokes equations are fully transformed in the new coordinate system while including the independent variables, the velocity components as well as the directions in which the momentum equations are applicable. A non-staggered grid system is used for all variables by substituting the continuity equation with the Pressure Poisson Equation and its appropriate boundary conditions. The flow problem is solved for various skew angles of the cavity. The transformed energy equation is also numerically solved to predict the temperature field in the skewed cavities for different heating conditions at the cavity walls. The present study provides simplifications in numerical modelling of the flow system in cavities without large skewness. In addition, a good agreement is found with previously reported results for skew angles equal to or closer to 90 degrees.