The increase in frequency and intensity of extreme precipitation events caused by the changing climate (e.g., cloudbursts, rainstorms, heavy rainfall, hail, heavy snow), combined with the high population density and concentration of assets, makes urban areas particularly vulnerable to pluvial flooding. Hence, assessing their vulnerability under current and future climate scenarios is of paramount importance. Detailed hydrologic-hydraulic numerical modeling is resource intensive and therefore scarcely suitable for performing consistent hazard assessments across large urban settlements. Given the steadily increasing availability of LiDAR (Light Detection And Ranging) high-resolution DEMs (Digital Elevation Models), several studies highlighted the potential of fast-processing DEM-based methods, such as the Hierarchical Filling-&-Spilling or Puddle-to-Puddle Dynamic Filling-&-Spilling Algorithms (abbreviated herein as HFSAs). We develop a fast-processing HFSA, named Safer_RAIN, that enables mapping of pluvial flooding in large urban areas by accounting for spatially distributed rainfall input and infiltration processes through a pixel-based Green-Ampt model. We present the first applications of the algorithm to two case studies in Northern Italy. Safer_RAIN output is compared against ground evidence and detailed output from a two-dimensional (2D) hydrologic and hydraulic numerical model (overall index of agreement between Safer_RAIN and 2D benchmark model: sensitivity and specificity up to 71% and 99%, respectively), highlighting potential and limitations of the proposed algorithm for identifying pluvial flood-hazard hotspots across large urban environments.