Quantum-state-resolved reactive-scattering dynamics of F+D(2)O-->DF+OD have been studied at E(c.m.)=5(1) kcal/mol in low-density crossed supersonic jets, exploiting pulsed discharge sources of F atom and laser-induced fluorescence to detect the nascent OD product under single-collision conditions. The product OD is formed exclusively in the v(OD)=0 state with only modest rotational excitation (<E(rot)> =0.50(1) kcal/mol), consistent with the relatively weak coupling of the 18.1(1) kcal/mol reaction exothermicity into "spectator" bond degrees of freedom. The majority of OD products [68(1)%] are found in the ground ((2)Pi(32) (+/-)) spin-orbit state, which adiabatically correlates with reaction over the lowest and only energetically accessible barrier (DeltaE( not equal) approximately 4 kcal/mol). However, 32(1)% of molecules are produced in the excited spin-orbit state ((2)Pi(12) (+/-)), although from a purely adiabatic perspective, this requires passage over a DeltaE( not equal) approximately 25 kcal/mol barrier energetically inaccessible at these collision energies. This provides unambiguous evidence for nonadiabatic surface hopping in F+D(2)O atom abstraction reactions, indicating that reactive-scattering dynamics even in simple atom+polyatom systems is not always isolated on the ground electronic surface. Additionally, the nascent OD rotational states are well fitted by a two-temperature Boltzmann distribution, suggesting correlated branching of the reaction products into the DF(v=2,3) vibrational manifold.