Many everyday mobile manipulation tasks require precise interaction with small objects, such as grasping a knob to open a cabinet or pressing a light switch. In this paper, we develop Servoing with Vision Models (SVM), a closed-loop training-free framework that enables a mobile manipulator to tackle such precise tasks involving the manipulation of small objects. SVM employs an RGB-D wrist camera and uses visual servoing for control. Our novelty lies in the use of state-of- the-art vision models to reliably compute 3D targets from the wrist image for diverse tasks and under occlusion due to the end-effector. To mitigate occlusion artifacts, we employ vision models to out-paint the end-effector thereby significantly en- hancing target localization. We demonstrate that aided by out- painting methods, open-vocabulary object detectors can serve as a drop-in module to identify semantic targets (e.g. knobs) and point tracking methods can reliably track interaction sites indicated by user clicks. This training-free method obtains an 85% zero-shot success rate on manipulating unseen objects in novel environments in the real world, outperforming an open- loop control method and an imitation learning baseline trained on 1000+ demonstrations by an absolute success rate of 50%.