We show that quantum entanglement, nowadays so widely observed and used in a multitude of systems, can be traced in the atomic spins of metal clusters supported on metal surfaces. Most importantly, we show that it can be voluntarily altered with external electric fields. We use a combination of ab initio and model Heisenberg-Dirac-Van Vleck quantum spin Hamiltonian calculations to show, with the example of a prototype system (Mn dimers on Ag(001) surface), that, in an inherently unentangled system an electric field can "switch on" the entanglement and significantly change its critical temperature parameter. The physical mechanism allowing such rigorous control of entanglement by an electric field is the field-induced change in the internal magnetic coupling of the supported nanostructure.