Precise manipulation that is generalizable across scenes and objects remains a persistent challenge in robotics. Current approaches for this task heavily depend on having a significant number of training instances to handle objects with pronounced visual and/or geometric part ambiguities. Our work explores the grounding of fine-grained part descriptors for precise manipulation in a zero-shot setting by utilizing web-trained text-to-image diffusion-based generative models. We tackle the problem by framing it as a dense semantic part correspondence task. Our model returns a gripper pose for manipulating a specific part, using as reference a user-defined click from a source image of a visually different instance of the same object. We require no manual grasping demonstrations as we leverage the intrinsic object geometry and features. Practical experiments in a real-world tabletop scenario validate the efficacy of our approach, demonstrating its potential for advancing semantic-aware robotics manipulation. Web page: https://tsagkas.github.io/click2grasp