Talking Head Generation aims at synthesizing natural-looking talking videos from speech and a single portrait image. Previous 3D talking head generation methods have relied on domain-specific heuristics such as warping-based facial motion representation priors to animate talking motions, yet still produce inaccurate 3D avatar reconstructions, thus undermining the realism of generated animations. We introduce Splat-Portrait, a Gaussian-splatting-based method that addresses the challenges of 3D head reconstruction and lip motion synthesis. Our approach automatically learns to disentangle a single portrait image into a static 3D reconstruction represented as static Gaussian Splatting, and a predicted whole-image 2D background. It then generates natural lip motion conditioned on input audio, without any motion driven priors. Training is driven purely by 2D reconstruction and score-distillation losses, without 3D supervision nor landmarks. Experimental results demonstrate that Splat-Portrait exhibits superior performance on talking head generation and novel view synthesis, achieving better visual quality compared to previous works. Our project code and supplementary documents are public available at https://github.com/stonewalking/Splat-portrait.