A search is presented for an excess of events with heavy-flavor quark pairs (tt-bar and bb-bar) and a large imbalance in transverse momentum in data from proton-proton collisions at a center-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 2.2 inverse femtobarns collected with the CMS detector at the CERN LHC. No deviations are observed with respect to standard model predictions. The results are used in the first interpretation of dark matter production in tt-bar and bb-bar final states in a simplified model. This analysis is also the first to perform a statistical combination of searches for dark matter produced with different heavy-flavor final states. The combination provides exclusions that are stronger than those achieved with individual heavy-flavor final states.