A data sample containing top quark pairs (tt over bar ) produced in association with a Lorentz-boosted Z or Higgs boson is used to search for signs of new physics using effective field theory. The data correspond to an integrated luminosity of 138 fb-1 of proton-proton collisions produced at a center-of-mass energy of 13 TeV at the LHC and collected by the CMS experiment. Selected events contain a single lepton and hadronic jets, including two identified with the decay of bottom quarks, plus an additional large-radius jet with high transverse momentum identified as a Z or Higgs boson decaying to a bottom quark pair. Machine learning techniques are employed to discriminate between tt over bar Z or tt over bar H events and events from background processes, which are dominated by tt over bar + jets production. No indications of new physics are observed. The signal strengths of boosted tt over bar Z and tt over bar H production are measured, and upper limits are placed on the tt over bar Z and tt over bar H differential cross sections as functions of the Z or Higgs boson transverse momentum. The effects of new physics are probed using a framework in which the standard model is considered to be the low-energy effective field theory of a higher energy scale theory. Eight possible dimension-six operators are added to the standard model Lagrangian, and their corresponding coefficients are constrained via fits to the data.