Context : NGC346-013 is a peculiar double-lined eclipsing binary in the Small Magellanic Cloud ( SMC ) discovered by the VLT-FLAMES survey of massive stars . Aims : We use spectroscopic and photometric observations to investigate the physical properties and evolutionary history of NGC346-013 . Methods : Spectra obtained with VLT/FLAMES are used to construct a radial velocity curve for NGC346-013 and to characterise the early B-type secondary . Photometry obtained with the Faulkes Telescope South is then used to derive orbital parameters , while spectra of the secondary are compared with synthetic spectra from TLUSTY model atmospheres . Results : The orbital period is found to be 4.20381 ( 12 ) days , with masses of 19.1 \pm 1.0 and 11.9 \pm 0.6 M _ { \odot } . The primary is a rapidly rotating ( v _ { \text { rot } } = 320 \pm 30 \mbox { km~ { } s } ^ { -1 } ) late-O dwarf while the secondary , an early-B giant , displays synchronous rotation and has filled its Roche lobe , implying that it was originally the more massive component with recent mass transfer ‘ spinning up ’ the primary to near-critical rotation . Comparison with synthetic spectra finds temperatures of 34.5kK and 24.5kK for the primary and secondary respectively , with the nitrogen abundance of the secondary enhanced compared to baseline values for the SMC , consistent with the predictions of models of interacting binaries . Conclusions : NGC346-013 likely evolved via non-conservative mass transfer in a system with initial masses \sim 22+15 M _ { \odot } , with the well-constrained orbital solution and atmospheric parameters making it an excellent candidate for tailored modelling with binary evolution codes . This system will form a cornerstone in constraining the physics of thermal timescale mass transfer , and the associated mass transfer efficiency , in massive close binary systems .