We report final-state-exclusive measurements of the light charged fragments in coincidence with (26)Ne residual nuclei following the direct two-proton removal from a neutron-rich (28)Mg secondary beam. A Dalitz-plot analysis and comparisons with simulations show that a majority of the triple-coincidence events with two protons display phase-space correlations consistent with the (two-body) kinematics of a spatially correlated pair-removal mechanism. The fraction of such correlated events, 56(12)%, is consistent with the fraction of the calculated cross section, 64%, arising from spin S=0 two-proton configurations in the entrance-channel (shell-model) (28)Mg ground state wave function. This result promises access to an additional and more specific probe of the spin and spatial correlations of valence nucleon pairs in exotic nuclei produced as fast secondary beams.