Contact.Spectropolarimetric reconstructions of the photospheric vector magnetic field are intrinsically limited by the 180° ambiguity in the orientation of the transverse component. So far, the removal of such an ambiguity has required assumptions about the properties of the photospheric field, which makes disambiguation methods model-dependent. Aims. The successful launch and operation of Solar Orbiter have made the removal of the 180° ambiguity possible solely using observations of the same location on the Sun obtained from two different vantage points. Methods. The basic idea is that the unambiguous line-of-sight component of the field measured from one vantage point will generally have a nonzero projection on the ambiguous transverse component measured by the second telescope, thereby determining the 'true' orientation of the transverse field. Such an idea was developed and implemented as part of the stereoscopic disambiguation method (SDM), which was recently tested using numerical simulations. Results. In this work we present a first application of the SDM to data obtained by the High Resolution Telescope (HRT) on board Solar Orbiter during the March 2022 campaign, when the angle with Earth was 27 degrees. The method was successfully applied to remove the ambiguity in the transverse component of the vector magnetogram solely using observations (from HRT and from the Helioseismic and Magnetic Imager) for the first time. Conclusions. The SDM is proven to provide observation-only disambiguated vector magnetograms that are spatially homogeneous and consistent. A discussion on the sources of error that may limit the accuracy of the method, and strategies to remove them in future applications, is also presented.