Class imbalance is prevalent in real-world node classification tasks and poses great challenges for graph machine-learning models. Most existing studies are rooted in a class-rebalancing (CR) perspective and aim to address class imbalance with class-wise reweighting or resampling. In this work, we approach the root cause of class-imbalance bias from an orthogonal topological paradigm. Specifically, we theoretically reveal and empirically observe two fundamental phenomena in the underlying graph topology that can greatly exacerbate the predictive bias stemming from class imbalance. In light of these findings, we devise a lightweight topological augmentation framework called TOBE to mitigate the class-imbalance bias without class rebalancing. Being orthogonal to CR, the proposed TOBE is a model-agnostic and efficient solution that can be seamlessly combined with and further boost existing CR techniques. Systematic experiments on real-world imbalanced graph learning tasks show that TOBE can deliver up to 46.27% performance gain and up to 72.74% bias reduction over existing techniques. Code is available at https://anonymous.4open.science/r/ToBE/.