Superconductivity at the LaTiO3/SrTiO3 interface is studied by low temperature and high magnetic field measurements as a function of a back-gate voltage. We show that it is intimately related to the appearance of a low density (a few 1012 cm-2) of high mobility carriers, in addition to low mobility ones always present in the system. These carriers form superconducting puddles coupled by a metallic two-dimensional electron gas, as revealed by the analysis of the phase transition driven by a perpendicular magnetic field. Two critical fields are evidenced, and a quantitative comparison with a recent theoretical model is made. © Published under licence by IOP Publishing Ltd.