Ancient mass extinction events such as the end-Permian and end-Triassic crises provide analogues for multistressor global change of ocean warming, pH reduction, and deoxygenation. Organism physiology is hypothesized to be a key trait influencing vulnerability to these stressors, but it is not certain how physiology predicts survival over evolutionary time scales and when organisms are faced with opposing or synergistic stressors. Fishes (bony fishes and chondrichthyan fishes) are active organisms with high aerobic scope for thermal tolerance and well-developed acid-base regulation, traits that should confer resilience to global change. To test this, we compiled a database of fossil marine fish occurrences to quantify extinction rates during background and mass extinctions from the Permian through Early Jurassic, using maximum likelihood estimation to compare extinction trajectories with marine invertebrates. Our results show that fewer chondrichthyan fishes underwent extinction than marine invertebrates during the end-Permian crisis. End-Triassic chondrichthyan extinction rates also were not elevated above background levels. In contrast, bony fishes underwent an end-Triassic extinction comparable to that of marine invertebrates. The differing responses of these two groups imply that a more active physiology can be advantageous during global change, although not uniformly. Permian–Triassic chondrichthyan fishes may have had broader environmental tolerances, facilitating survival. Alternatively, the larger offspring size of chondrichthyan fishes may provide greater energy reserves to offset the demands of warming and acidification. Although more active organisms have adult adaptations for thermal tolerance and pH regulation, some may nevertheless be susceptible to global change during early life stages.