Cyclones can cause mass mortality of seabirds, sometimes wrecking thousands of individuals. The few studies to track pelagic seabirds during cyclones show they tend to circumnavigate the strongest winds. We tracked adult shearwaters in the Sea of Japan over 11 y and found that the response to cyclones varied according to the wind speed and direction. In strong winds, birds that were sandwiched between the storm and mainland Japan flew away from land and toward the eye of the storm, flying within ≤30 km of the eye and tracking it for up to 8 h. This exposed shearwaters to some of the highest wind speeds near the eye wall (≤21 m s) but enabled them to avoid strong onshore winds in the storm's wake. Extreme winds may therefore become a threat when an inability to compensate for drift could lead to forced landings and collisions. Birds may need to know where land is in order to avoid it. This provides additional selective pressure for a map sense and could explain why juvenile shearwaters, which lack a map sense, instead navigating using a compass heading, are susceptible to being wrecked. We suggest that the ability to respond to storms is influenced by both flight and navigational capacities. This may become increasingly pertinent due to changes in extreme weather patterns.