SuperCDMS is an experiment designed to directly detect Weakly Interacting Massive Particles (WIMPs), a favored candidate for dark matter ubiquitous in the Universe. In this paper, we present WIMP-search results using a calorimetric technique we call CDMSlite, which relies on voltage- assisted Luke-Neganov amplification of the ionization energy deposited by particle interactions. The data were collected with a single 0.6 kg germanium detector running for 10 live days at the Soudan Underground Laboratory. A low energy threshold of 170 eVee (electron equivalent) was obtained, which allows us to constrain new WIMP-nucleon spin-independent parameter space for WIMP masses below 6 GeV/c2.