Genetic evidence indicates that Saccharomyces cerevisiae Sgs1, Top3, and Rmi1 resolve topologically linked intermediates arising from DNA replication and recombination. Using purified proteins, we show that Sgs1, Top3, Rmi1, and replication protein A (RPA) coordinate catenation and decatenation of dsDNA through sequential passage of single strands of DNA, establishing a unique pathway for dsDNA decatenation in eukaryotic cells. Sgs1 is required for dsDNA unwinding and, unexpectedly, also has a structural role in DNA strand passage. RPA promotes DNA unwinding by Sgs1 by trapping ssDNA, and it stimulates DNA strand passage by Top3. Paradoxically, Rmi1 has a unique regulatory capacity that slows DNA relaxation by Top3 but stimulates DNA decatenation. We establish that Rmi1 stabilizes the "open" Top3-DNA covalent complex formed as a transient intermediate of strand passage. This concerted activity of the Sgs1-Top3-Rmi1-RPA represents an important mechanism for disentangling structures resulting from the topological features of duplex DNA.