We investigate the integration of visual and tactile sensory input for dynamic manipulation. Our experimental data and computational modeling reveal that time-delays are as critical to task-optimal multisensory integration as sensorimotor noise. Our focus is a dynamic manipulation task "at the edge of instability." Mathematical bifurcation theory predicts that this system will exhibit well-classified low-dimensional dynamics in this regime. The task was using the thumbpad to compress a slender spring prone to buckling as far as possible, just shy of slipping. As expected from bifurcation theory, principal components analysis gives a projection of the data onto a low dimensional subspace that captures 91-97% of its variance. In this subspace, we formulate a low-order model for the brain+hand+spring dynamics based on known mechanical and neurophysiological properties of the system. By systematically occluding vision and anesthetically blocking thumbpad sensation in 12 consenting subjects, we found that vision contributed to dynamic manipulation only when thumbpad sensation was absent. The reduced ability of the model system to compress the spring with absent sensory channels closely resembled the experimental results. Moreover, we found that the model reproduced the contextual usefulness of vision only if we took account of time-delays. Our results shed light on critical features of dynamic manipulation distinct from those of static pinch, as well as the mechanism likely responsible for loss of manual dexterity and increased reliance on vision when age or neuromuscular disease increase noisiness and/or time-delays during sensorimotor integration.