Abstract: We discuss FLRW-cosmologies with negatively-curved spatial slices that induce a late-time stabilization of all the moduli of an effective field theory through Hubble friction, independently of the moduli-space curvature. This holds for pure moduli, which appear ubiquitously in string compactifications. Crucially, the cosmological solutions approach a Milne universe. Hence, the mechanism we describe in fact corresponds to late-time moduli stabilization in Minkowski spacetime.