Using the fusion-evaporation reaction ^{106}Cd(^{58}Ni,4n)^{160}Os and the gas-filled recoil separator SHANS, two new isotopes _{76}^{160}Os and _{74}^{156}W have been identified. The α decay of ^{160}Os, measured with an α-particle energy of 7080(26) keV and a half-life of 201_{-37}^{+58} μs, is assigned to originate from the ground state. The daughter nucleus ^{156}W is a β^{+} emitter with a half-life of 291_{-61}^{+86} ms. The newly measured α-decay data allow us to derive α-decay reduced widths (δ^{2}) for the N=84 isotones up to osmium (Z=76), which are found to decrease with increasing atomic number above Z=68. The reduction of δ^{2} is interpreted as evidence for the strengthening of the N=82 shell closure toward the proton drip line, supported by the increase of the neutron-shell gaps predicted in theoretical models.