We study the spin-splitting in the spectrum of heavy quarkonium hybrids using non-relativistic effective theory. After sequentially integrating out modes at the scales m_Q, m_Q v and Lambda_QCD, we obtain the spin-dependent potential to order 1/m_Q^2, in which non-perturbative contributions are given by gluonic correlators. With the hybrid potentials obtained from the lattice, we solve the relevant Schrodinger equation in the EFT, and obtain the spin-splitting by applying perturbation theory. Values of non-perturbative contributions are obtained by fitting to lattice data of the charmonium hybrid spectrum. With these non-perturbative parameters obtained, we predict the bottomonium hybrid spectrum.