In 2D systems, ecosystem size, or spatial scale, has been considered a general predictor of various ecological properties. An outstanding example is the spatial scaling of metapopulation stability: theory predicts that metapopulation stability should increase with ecosystem size, because larger ecosystems will harbor more diverse subpopulations with more stable aggregate dynamics. However, scale-invariant complexity of ecosystems — an underappreciated, but widespread feature of ecosystems — can also serve as the physical template that underpins diversity of population dynamics in a metapopulation. Here, I combine theory and analyses of a unique long-term dataset to show that a scale-invariant characteristic of fractal river networks, branching complexity, stabilizes watershed metapopulations. Theory predicted that the stabilizing effect of branching complexity can be a consequence of purely stochastic processes. Contrary to current theories developed in 2D systems, metapopulation size had vague effects on metapopulation stability. These theoretical predictions were supported by 18-y observations of fish populations across 31 watersheds. Our cross-watershed comparisons revealed consistent stabilizing effects of branching complexity on metapopulations of very different riverine fishes. A strong association between branching complexity and metapopulation stability is likely to be a pervasive feature of branching networks that strongly affects species persistence.