The PHENIX experiment has measured open heavy-flavor production via semileptonic decay over the transverse momentum range 1 < p(T) < 6 GeV/c at forward and backward rapidity (1.4 < vertical bar y vertical bar < 2.0) in d + Au and p + p collisions at root s(NN) = 200 GeV. In central d + Au collisions, relative to the yield in p + p collisions scaled by the number of binary nucleon-nucleon collisions, a suppression is observed at forward rapidity (in the d-going direction) and an enhancement at backward rapidity (in the Au-going direction). Predictions using nuclear-modified-parton-distribution functions, even with additional nuclear-p(T) broadening, cannot simultaneously reproduce the data at both rapidity ranges, which implies that these models are incomplete and suggests the possible importance of final-state interactions in the asymmetric d + Au collision system. These results can be used to probe cold-nuclear-matter effects, which may significantly affect heavy-quark production, in addition to helping constrain the magnitude of charmonia-breakup effects in nuclear matter.