3D Gaussian Splatting (3DGS) renders pixels by rasterizing Gaussian primitives, where conditional alpha-blending dominates the computational cost in the rendering pipeline. This paper proposes TC-GS, an algorithm-independent universal module that expands the applicability of Tensor Core (TCU) for 3DGS, leading to substantial speedups and seamless integration into existing 3DGS optimization frameworks. The key innovation lies in mapping alpha computation to matrix multiplication, fully utilizing otherwise idle TCUs in existing 3DGS implementations. TC-GS provides plug-and-play acceleration for existing top-tier acceleration algorithms and integrates seamlessly with rendering pipeline designs, such as Gaussian compression and redundancy elimination algorithms. Additionally, we introduce a global-to-local coordinate transformation to mitigate rounding errors from quadratic terms of pixel coordinates caused by Tensor Core half-precision computation. Extensive experiments demonstrate that our method maintains rendering quality while providing an additional 2.18x speedup over existing Gaussian acceleration algorithms, thereby achieving a total acceleration of up to 5.6x.