Hyperspectral image fusion aims to reconstruct high-spatial-resolution hyperspectral images (HR-HSI) by integrating complementary information from multi-source inputs. Despite recent progress, existing methods still face two critical challenges: (1) inadequate reconstruction of anisotropic spatial structures, resulting in blurred details and compromised spatial quality; and (2) spectral distortion during fusion, which hinders fine-grained spectral representation. To address these issues, we propose \textbf{ASSR-Net}: an Anisotropic Structure-Aware and Spectrally Recalibrated Network for Hyperspectral Image Fusion. ASSR-Net adopts a two-stage fusion strategy comprising anisotropic structure-aware spatial enhancement (ASSE) and hierarchical prior-guided spectral calibration (HPSC). In the first stage, a directional perception fusion module adaptively captures structural features along multiple orientations, effectively reconstructing anisotropic spatial patterns. In the second stage, a spectral recalibration module leverages the original low-resolution HSI as a spectral prior to explicitly correct spectral deviations in the fused results, thereby enhancing spectral fidelity. Extensive experiments on various benchmark datasets demonstrate that ASSR-Net consistently outperforms state-of-the-art methods, achieving superior spatial detail preservation and spectral consistency.