The selectivity of Watson-Crick base pairing has allowed the design of DNA-based functional materials bearing an unprecedented level of accuracy. Examples include DNA origami, made of tiles assembling into arbitrarily complex shapes, and DNA coated particles featuring rich phase behaviors. Frequently, the realization of conceptual DNA-nanotechnology designs has been hampered by the lack of strategies for effectively controlling relaxations. In this article, we address the problem of kinetic control on DNA-mediated interactions between Brownian objects. We design a kinetic pathway based on toehold-exchange mechanisms that enables rearrangement of DNA bonds without the need for thermal denaturation, and test it on suspensions of DNA-functionalized liposomes, demonstrating tunability of aggregation rates over more than 1 order of magnitude. While the possibility to design complex phase behaviors using DNA as a glue is already well recognized, our results demonstrate control also over the kinetics of such systems.