Summary Conservation of threatened species relies on predictions about their spatial distribution; however, it is often difficult to detect species in the wild. The combination of acoustic monitoring to improve species detectability and statistical methods to account for false‐negative detections can improve species distribution estimates. Here, we combine a novel automated species‐specific identification approach with occupancy models that account for imperfect detectability to provide a more accurate species distribution map of the Elfin Woods Warbler Setophaga angelae, a rare, elusive and threatened bird species. We also compared three automated species identification/validation approaches to determine which approach provided occupancy estimates similar to manual validation of all recordings. Acoustic data were collected along three elevational gradients (95–1074 m a.s.l) in El Yunque National Forest, Puerto Rico. The detection matrices acquired through automated species‐specific identification models and manual validations of all recordings were used to create occupancy models. Although this species has a wider distribution than previously reported, it depends on Palo Colorado forest cover and it mainly occurs between 600 and 900 m a.s.l. Unbiased and precise occupancy models were developed by using automated species identification models and only manually validating 4% of the recordings. Our approach draws on the strength of two active areas of ecological research: acoustic monitoring and occupancy modelling. Our methods provide an effective and efficient way to translate the enormous amount of acoustic information collected with passive acoustic monitoring devices into meaningful ecological data that can be applied to understand and map the distribution of rare, elusive and threatened species.