We present a factorization theorem for non-global observables at hadron colliders, such as gap-between-jets cross sections. The theorem factorizes cross sections into hard functions and low-energy matrix elements, which obey a renormalization group evolution equation. We detail the derivation of the associated anomalous dimension at one loop and show how it can be used to resum the leading double-logarithmic contributions to these cross sections to all orders, thereby solving the long-standing problem of all-order resummation for these so-called "super-leading logarithms". We also explain why the super-leading effects are sizable for pp→2 jets processes but suppressed in H/Z and H/Z+jet production.