Vision Foundation Models (VFMs) have achieved remarkable success when applied to various downstream 2D tasks. Despite their effectiveness, they often exhibit a critical lack of 3D awareness. To this end, we introduce Splat and Distill, a framework that instills robust 3D awareness into 2D VFMs by augmenting the teacher model with a fast, feed-forward 3D reconstruction pipeline. Given 2D features produced by a teacher model, our method first lifts these features into an explicit 3D Gaussian representation, in a feedforward manner. These 3D features are then ``splatted" onto novel viewpoints, producing a set of novel 2D feature maps used to supervise the student model, ``distilling" geometrically grounded knowledge. By replacing slow per-scene optimization of prior work with our feed-forward lifting approach, our framework avoids feature-averaging artifacts, creating a dynamic learning process where the teacher's consistency improves alongside that of the student. We conduct a comprehensive evaluation on a suite of downstream tasks, including monocular depth estimation, surface normal estimation, multi-view correspondence, and semantic segmentation. Our method significantly outperforms prior works, not only achieving substantial gains in 3D awareness but also enhancing the underlying semantic richness of 2D features. Project page is available at https://davidshavin4.github.io/Splat-and-Distill/