The kinetic stability of non-covalent macromolecular complexes controls many biological phenomena. Here we find that physical models of complex dissociation predict that competitor molecules will, in general, accelerate the breakdown of isolated bimolecular complexes by occluding rapid rebinding of the two binding partners. This prediction is largely independent of molecular details. We confirm the prediction with single-molecule fluorescence experiments on a well-characterized DNA strand dissociation reaction. Contrary to common assumptions, competitor-induced acceleration of dissociation can occur in biologically relevant competitor concentration ranges and does not necessarily imply ternary association of competitor with the bimolecular complex. Thus, occlusion of complex rebinding may play a significant role in a variety of biomolecular processes. The results also show that single-molecule colocalization experiments can accurately measure dissociation rates despite their limited spatiotemporal resolution.