The lissencephaly protein Lis1 has been reported to regulate the mechanical behavior of cytoplasmic dynein, the primary minus-end-directed microtubule motor. However, the regulatory mechanism remains poorly understood. Here, we address this issue using purified proteins from Saccharomyces cerevisiae and a combination of techniques, including single-molecule imaging and single-particle electron microscopy. We show that rather than binding to the main ATPase site within dynein's AAA+ ring or its microtubule-binding stalk directly, Lis1 engages the interface between these elements. Lis1 causes individual dynein motors to remain attached to microtubules for extended periods, even during cycles of ATP hydrolysis that would canonically induce detachment. Thus, Lis1 operates like a "clutch" that prevents dynein's ATPase domain from transmitting a detachment signal to its track-binding domain. We discuss how these findings provide a conserved mechanism for dynein functions in living cells that require prolonged microtubule attachments.