Traditionally, modelling panels with curvilinear stiffeners using the Ritz method requires two separate domains: a 2D plate domain for the skin and a 1D beam domain for the stiffeners. These domains are then assembled to determine the overall structural response. In this article, a novel single-domain Ritz-based approach is proposed for the semi-analytical modelling of curvilinearly grid-stiffened panels. A variable-stiffness domain is constructed to represent a skin concentrically stiffened by an arbitrary number of tow-placed curvilinear stiffeners, which share the same stacking direction as the skin. The proposed approach is implemented for addressing the buckling problem of panels with curvilinear fibres and stiffeners based on the first-order shear deformation theory. Prebuckling and buckling responses are derived using the principles of stationary complementary energy and total potential energy, respectively. The elements of the resulting matrices are computed through a specialized numerical integration strategy based on the Romberg integration rule. The quality of the results obtained with the proposed approach is validated by comparison with finite element simulations. The results demonstrate good agreement, highlighting the potential of the developed approach as a valuable tool for modelling curvilinearly grid-stiffened panels and conducting preliminary parametric and design optimization studies.