Noble-gas spins feature hours-long coherence times, owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically excited potassium atoms and reveal the formation of quasibound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to 6 orders of magnitude and 2 orders of magnitude enhancement for the thermally averaged, polarization rate coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.