Anonymous web-based experiments are increasingly and successfully used in many domains of behavioral research. However, online studies of auditory perception, especially of psychoacoustic phenomena pertaining to low-level sensory processing, are challenging because of limited available control of the acoustics, and the unknown hearing status of participants. Here, we outline our approach to mitigate these challenges and validate our procedures by comparing web-based measurements to lab-based data on a range of classic psychoacoustic tasks. Individual tasks were created using jsPsych, an open-source javascript front-end library. Dynamic sequences of psychoacoustic tasks were implemented using Django, an open-source library for web applications, and combined with consent pages, questionnaires, and debriefing pages. Subjects were recruited via Prolific, a web-based human-subject marketplace. Guided by a meta-analysis of normative data, we developed and validated a screening procedure to select participants for (putative) normal-hearing status; this procedure combined thresholding of scores in a suprathreshold cocktail-party task with filtering based on survey responses. Headphone use was standardized by supplementing procedures from prior literature with a binaural hearing task. Individuals meeting all criteria were re-invited to complete a range of classic psychoacoustic tasks. Performance trends observed in re-invited participants were in excellent agreement with lab-based data for fundamental frequency discrimination, gap detection, sensitivity to interaural time delay and level difference, comodulation masking release, word identification, and consonant confusions. Our results suggest that web-based psychoacoustics is a viable complement to lab-based research. Source code for our infrastructure is also provided.