The performance capabilities of flying animals reflect the interplay of biomechanical and physiological constraints and evolutionary innovation. Of the two extant groups of vertebrates that are capable of powered flight, birds are thought to fly more efficiently and faster than bats. However, fast-flying bat species that are adapted for flight in open airspace are similar in wing shape and appear to be similar in flight dynamics to fast-flying birds that exploit the same aerial niche. Here, we investigate flight behaviour in seven free-flying Brazilian free-tailed bats (Tadarida brasiliensis) and report that the maximum ground speeds achieved exceed speeds previously documented for any bat. Regional wind modelling indicates that bats adjusted flight speeds in response to winds by flying more slowly as wind support increased and flying faster when confronted with crosswinds, as demonstrated for insects, birds and other bats. Increased frequency of pauses in wing beats at faster speeds suggests that flap-gliding assists the bats' rapid flight. Our results suggest that flight performance in bats has been underappreciated and that functional differences in the flight abilities of birds and bats require re-evaluation.