Segmenting unknown or anomalous object instances is a critical task in autonomous driving applications, and it is approached traditionally as a per-pixel classification problem. However, reasoning individually about each pixel without considering their contextual semantics results in high uncertainty around the objects' boundaries and numerous false positives. We propose a paradigm change by shifting from a per-pixel classification to a mask classification. Our mask-based method, Mask2Anomaly, demonstrates the feasibility of integrating a mask-classification architecture to jointly address anomaly segmentation, open-set semantic segmentation, and open-set panoptic segmentation. Mask2Anomaly includes several technical novelties that are designed to improve the detection of anomalies/unknown objects: i) a global masked attention module to focus individually on the foreground and background regions; ii) a mask contrastive learning that maximizes the margin between an anomaly and known classes; iii) a mask refinement solution to reduce false positives; and iv) a novel approach to mine unknown instances based on the mask- architecture properties. By comprehensive qualitative and qualitative evaluation, we show Mask2Anomaly achieves new state-of-the-art results across the benchmarks of anomaly segmentation, open-set semantic segmentation, and open-set panoptic segmentation. The code and pre-trained models are available: https://github.com/shyam671/Mask2Anomaly-Unmasking-Anomalies-in-Road-Scene-Segmentation/tree/main .