Mass loss is a key physical process in the evolution of massive stars, the impact of which propagates into galactic evolution, population synthesis models, the interpretation of high-redshift galaxies, and explosive events such as supernovae. However, there are currently substantial uncertainties in the low-metallicity, low-luminosity thin wind regime where classical diagnostics (H-alpha and ultraviolet, UV, P Cygni profiles) yield wind momenta that are 1 to 2 orders of magnitude below prescriptions implemented by default in most evolutionary models. Here, we present spectra of the mass-loss diagnostic line Br-alpha in 15 OB-type stars in the Small Magellanic Cloud obtained using the Near Infrared Spectrograph on the James Webb Space Telescope. The line profile morphology, recovered by virtue of the outstanding signal-to-noise ratio of the data and the avoidance of regions with nebular emission, is consistent with predictions based on previous mass-loss rate estimates from optical and UV spectroscopy. Moreover, an initial spectroscopic analysis of sources covering the thin wind regime confirms the low mass-loss rates, indicates a change of slope in the wind-momentum-luminosity relation in this regime with respect to high-luminosity objects, and strengthens the abovementioned discrepancies with commonly used wind-momentum prescriptions.