When catching a falling ball or avoiding a collision with traffic, humans can quickly generate eye and limb responses to unpredictable changes in their environment. Mechanisms of limb and oculomotor control when responding to sudden changes in the environment have mostly been investigated independently. Here, we investigated eye-hand coordination in a rapid interception task where human participants used a virtual paddle to intercept a moving target. The target moved vertically down a computer screen and could suddenly jump to the left or right. In high-certainty blocks, the target always jumped; in low-certainty blocks, the target only jumped in a portion of the trials. Further, we manipulated response urgency by varying the time of target jumps, with early jumps requiring less urgent responses and late jumps requiring more urgent responses. Our results highlight differential effects of certainty and urgency on eye-hand coordination. Participants initiated both eye and hand responses earlier for high-certainty compared with low-certainty blocks. Hand reaction times decreased and response vigor increased with increasing urgency levels. However, eye reaction times were lowest for medium-urgency levels and eye vigor was unaffected by urgency. Across all trials, we found a weak positive correlation between eye and hand responses. Taken together, these results suggest that the limb and oculomotor systems use similar early sensorimotor processing; however, rapid responses are modulated differentially to attain system-specific sensorimotor goals.