We report the results of a 1998 July BeppoSAX observation of a field in the Small Magellanic Cloud which led to the discovery of approximately 345 s pulsations in the X-ray flux of SAX J0103.2-7209. The BeppoSAX X-ray spectrum is well fitted by an absorbed power law with a photon index of approximately 1.0 plus a blackbody component with kT=0.11 keV. The unabsorbed luminosity in the 2-10 keV energy range is approximately 1.2x1036 ergs s-1. In a very recent Chandra observation, the 345 s pulsations are also detected. The available period measurements provide a constant period derivative of -1.7 s yr-1 over the last 3 years, making SAX J0103.2-7209 one of the most rapidly spinning up X-ray pulsars known. The BeppoSAX position (30&arcsec; uncertainty radius) is consistent with that of the Einstein source 2E 0101.5-7225 and the ROSAT source RX J0103.2-7209. This source was detected at a luminosity level of a few times 1035-1036 ergs s-1 in all data sets of past X-ray missions since 1979. The ROSAT HRI and Chandra positions are consistent with that of a mV=14.8 Be spectral-type star already proposed as the likely optical counterpart of 2E 0101.5-7225. We briefly report and discuss photometric and spectroscopic data carried out at the ESO telescopes 2 days before the BeppoSAX observation. We conclude that SAX J0103.2-7209 and 2E 0101.5-7225 are the same source: a relatively young and persistent X-ray pulsar in the SMC.