The cross sections of nuclear reactions between the radioisotope Be7 and deuterium, a possible mechanism of reducing the production of mass-7 nuclides in big-bang nucleosynthesis, were measured at center-of-mass energies between 0.2 and 1.5 MeV. The measured cross sections are dominated by the (d,α) reaction channel, towards which prior experiments were mostly insensitive. A new resonance at 0.36(5) MeV with a strength of ωγ=1.7(5)  keV was observed inside the relevant Gamow window. Calculations of nucleosynthesis outcomes based on the experimental cross section show that the resonance reduces the predicted abundance of primordial Li7, but not sufficiently to solve the primordial lithium problem.