We consider a system of two spins under a scanning tunneling microscope bias and derive its master equation. We find that the tunneling elements to the electronic contacts (tip and substrate) generate an exchange interaction between the spins, as well as a Dzyaloshinskii-Moriya interaction in the presence of spin-orbit coupling. The tunnel current spectrum then shows additional lines compared to conventional spin resonance experiments. When the spins have degenerate Larmor frequencies and equal tunneling amplitudes (without spin-orbit), there is a dark state with vanishing decay rate. The coupling to the electronic environment generates significant spin-spin entanglement via the dark state, even if the initial state is non-entangled.