Reducing deforestation underpins efforts to conserve global biodiversity. However, this focus on retaining forest cover overlooks the multitude of anthropogenic pressures that can degrade forest quality in ways that may imperil biodiversity. Here we use the latest remotely-sensed measures of forest structural condition and associated human pressures across the global humid tropics to provide the first estimates of the importance of forest quality, relative to forest cover, in mitigating extinction risk for rainforest vertebrates worldwide. We found tropical rainforests of intact structural condition and minimal human pressures played an outsized role in reducing the odds of species being threatened or having a declining population. Further, the effects of forest quality in mitigating extinction risk were stronger when small amounts of high quality forest remained within species geographic ranges, as opposed to when large extents were forested but of low quality. Our research underscores a critical need to focus global environmental policy and conservation strategies toward the targeted protection of the last remaining undisturbed forest landscapes, in concert with strategies aimed at preserving, restoring and reconnecting remnant forest fragments across the hyperdiverse humid tropics.