Fixed point theory has witnessed substantial development through the introduction of generalized metric structures. Among these, S-metric spaces and their rectangular variants have emerged as powerful frameworks for extending classical contraction principles. In this paper, we investigate common fixed point results in complete rectangular D-metric spaces, obtained through a structural reformulation of S-metric spaces. We establish a new contraction-type condition for a pair of self-mappings and prove the existence and uniqueness of a coincidence point under suitable range inclusion and completeness assumptions. Further, by employing weak compatibility of mappings, we derive the existence of a unique common fixed point. The presented theorem generalizes several known results in rectangular S-metric spaces and broadens the applicability of fixed point theory in generalized nonlinear structures. The results contribute to the ongoing development of metric-type spaces and their applications in nonlinear functional analysis.