We study the origin of broadening of superconducting transition in sputtered Nb films at high magnetic fields. From simultaneous tunneling and transport measurements we conclude that the upper critical field H-c2 always corresponds to the bottom of transition R similar to 0, while the top R similar to R-n occurs close to the critical field for destruction of surface superconductivity H-c3 similar or equal to 1.7H(c2). The two-dimensional nature of superconductivity at H > H-c2 is confirmed by cusplike angular dependence of magnetoresistance. Our data indicates that surface superconductivity is remarkably robust even in disordered polycrystalline films and, surprisingly, even in perpendicular magnetic fields. We conclude that surface superconductivity, rather than flux-flow phenomenon, inhomogeneity, or superconducting fluctuations, is the primary cause of broadening of superconducting transition in magnetic field.