Cohesin stably holds together the sister chromatids from S phase until mitosis. To do so, cohesin must be protected against its cellular antagonist Wapl. Eco1 acetylates cohesin's Smc3 subunit, which locks together the sister DNAs. We used yeast genetics to dissect how Wapl drives cohesin from chromatin and identified mutants of cohesin that are impaired in ATPase activity but remarkably confer robust cohesion that bypasses the need for the cohesin protectors Eco1 in yeast and Sororin in human cells. We uncover a functional asymmetry within the heart of cohesin's highly conserved ABC-like ATPase machinery and find that both ATPase sites contribute to DNA loading, whereas DNA release is controlled specifically by one site. We propose that Smc3 acetylation locks cohesin rings around the sister chromatids by counteracting an activity associated with one of cohesin's two ATPase sites.