The decay of excited states of the nucleus 135Sn, with three neutrons outside the doubly-magic 132Sn core, was studied in an experiment performed at the Radioactive Isotope Beam Factory at RIKEN. Several γ rays emitted from excited 135Sn ions were observed following one-neutron and one-neutron-one-proton removal from 136Sn and 137Sb beams, respectively, on a beryllium target at relativistic energies. Based on the analogy to 133Sn populated via one-neutron removal from 134Sn, an excitation energy of 695(15) keV is assigned to the 3/2− state with strongest single-particle character in 135Sn. This result provides the first direct information about the evolution of the neutron shell structure beyond N=82 and thus allows for a crucial test of shell-model calculations in this region. The experimental findings are in full agreement with calculations performed employing microscopic effective two-body interactions derived from CD-Bonn and N3LO nucleon-nucleon potentials, which do not predict a pronounced subshell gap at neutron number N=90. The occurrence of such a gap in 140Sn, i.e., when the 1f7/2 orbital is completely filled, had been proposed in the past, in analogy to the magicity of 48Ca, featuring a completely filled 0f7/2 orbital one harmonic oscillator shell below.