3D Gaussian Splatting has emerged as a powerful paradigm for explicit 3D scene representation, yet achieving efficient and consistent 3D segmentation remains challenging. Existing segmentation approaches typically rely on high-dimensional feature lifting, which causes costly optimization, implicit semantics, and task-specific constraints. We present \textbf{Segment Any Gaussians Online (SAGOnline)}, a unified, zero-shot framework that achieves real-time, cross-view consistent segmentation without scene-specific training. SAGOnline decouples the monolithic segmentation problem into lightweight sub-tasks. By integrating video foundation models (e.g., SAM 2), we first generate temporally consistent 2D masks across rendered views. Crucially, instead of learning continuous feature fields, we introduce a \textbf{Rasterization-aware Geometric Consensus} mechanism that leverages the traceability of the Gaussian rasterization pipeline. This allows us to deterministically map 2D predictions to explicit, discrete 3D primitive labels in real-time. This discrete representation eliminates the memory and computational burden of feature distillation, enabling instant inference. Extensive evaluations on NVOS and SPIn-NeRF benchmarks demonstrate that SAGOnline achieves state-of-the-art accuracy (92.7\% and 95.2\% mIoU) while operating at the fastest speed at 27 ms per frame. By providing a flexible interface for diverse foundation models, our framework supports instant prompt, instance, and semantic segmentation, paving the way for interactive 3D understanding in AR/VR and robotics.