The first search for supersymmetry in the vector-boson fusion topology is presented. The search targets final states with at least two leptons, large missing transverse momentum, and two jets with a large separation in rapidity. The data sample corresponds to an integrated luminosity of 19.7 fb⁻¹ of proton-proton collisions at (\sqrt{s})=8TeV collected with the CMS detector at the CERN LHC. The observed dijet invariant mass spectrum is found to be consistent with the expected standard model prediction. Upper limits are set on the cross sections for chargino and neutralino production with two associated jets, assuming the supersymmetric partner of the τ lepton to be the lightest slepton and the lightest slepton to be lighter than the charginos. For a so-called compressed-mass-spectrum scenario in which the mass difference between the lightest supersymmetric particle (\tilde{χ}_0^1) and the next lightest, mass-degenerate, gaugino particles (\tilde{χ}_0^2) and (\tilde{χ}_1^±) is 50 GeV, a mass lower limit of 170 GeV is set for these latter two particles.