The inhomogeneous 3 Kelvin phase is most likely a superconducting state nucleating at the interface between micrometer-sized Ru-metal inclusions and Sr2RuO4 above the bulk onset of superconductivity. This filamentary superconducting state yields a characteristic temperature dependence of the upper critical field which is sublinear, i.e., H-c2(T) alpha (T* - T)(gamma) with 0.5 < gamma < 1 (T*: nucleation temperature). The Ginzburg-Landau theory is used to analyze the behavior of the nucleated spin-triplet phase in a field and the characteristic features of H-c2 observed in the experiment are explained based on a two-component order parameter in the presence of a filament of enhanced superconductivity with a finite width.