The article addressed the Lagrange exponential stability of Cohen-Grossberg inertial neural networks (CGINNs) with quaternion-valued state variables and unbounded time-varying delays. The study extended stability analysis to a more complex and realistic model that included the inertial term, representing the system's acceleration-like memory effect, and quaternion-valued variables, representing multidimensional signals such as 3D rotations or color images. Unbounded time-varying delays added complexity while properly replicating real-world neural network (NN) dynamics. Unlike traditional studies that relied on order-reduction transformations, this work introduced a non-reduction order approach. To achieve stability, Lyapunov functional approaches were used with advanced inequality techniques to generate adequate criteria that ensured Lagrange stability under these complex conditions. Finally, Example 1 was presented to validate the efficiency of the proposed method, while Example 2, related to Quaternion-valued NNs (QVNNs), exhibited the efficiency of storing true color image patterns.