We present an updated search for the Higgs boson produced in association with a vector boson in the final state with missing transverse energy and two jets. We use the full CDF data set corresponding to an integrated luminosity of 9.45 fb−1 at a proton-antiproton center-of-mass energy of s√=1.96 TeV. New to this analysis is the inclusion of a b-jet identification algorithm specifically optimized for H→bb¯ searches. Across the Higgs boson mass range 90≤mH≤150 GeV/c2, the expected 95% credibility level upper limits on the VH production cross section times the H→bb¯ branching fraction are improved by an average of 14% relative to the previous analysis. At a Higgs boson mass of 125 GeV/c2, the observed (expected) limit is 3.06 (3.33) times the standard model prediction, corresponding to one of the most sensitive searches to date in this final state.