Quantum light is characterized by distinctive statistical distributions that are possible only because of quantum mechanical effects. For example, single photons and correlated photon pairs exhibit photon number distributions with variance lower than classically allowed limits. This enables high-fidelity transmission of quantum information and sensing with lower noise than possible with classical light sources(1,2). Most quantum light sources rely on spontaneous parametric processes such as down-conversion and four-wave mixing(2). These processes are mediated by vacuum fluctuations of the electromagnetic field. Therefore, by manipulating the electromagnetic mode structure, for example with dispersion-engineered nanophotonic systems, the spectrum of generated photons can be controlled(3-7). However, disorder, which is ubiquitous in nanophotonic fabrication, causes device-to-device spectral variations(8-11). Here we realize topologically robust electromagnetic modes and use their vacuum fluctuations to create a quantum light source in which the spectrum of generated photons is much less affected by fabrication-induced disorder. Specifically, we use the topological edge states realized in a two-dimensional array of ring resonators to generate correlated photon pairs by spontaneous four-wave mixing and show that they outperform their topologically trivial one-dimensional counterparts in terms of spectral robustness. We demonstrate the non-classical nature of the generated light and the realization of a robust source of heralded single photons by measuring the conditional antibunching of photons, that is, the reduced likelihood of photons arriving together compared to thermal or laser light. Such topological effects, which are unique to bosonic systems, could pave the way for the development of robust quantum photonic devices.