In the Atacama Desert, one of the driest places on Earth, the persistent absence of water preserves the record of environmental change, making it an invaluable proxy for studying the evolution of life on Earth. Due to the scarcity of in-situ measurements and difficulties in satellite remote sensing, information on precipitation characteristics is limited even for the present climate. Guided by a case study of extreme precipitation in late January 2019, we derive a conceptual framework to explain how moisture transport combined with the diurnal circulation produces rainfall. We found a synoptic pattern that we named "moist northerlies" (MNs) based on surface observations, reanalysis, and high-resolution simulation. During an MN event, moisture transport from the Tropical Pacific is observed in the lower free-troposphere in the forefront of an 850 hPa low-pressure offshore Atacama. The diurnal circulation (Rutllant Cell) transports the moist free tropospheric air inland above the coastal marine boundary layer, triggering clouds and storms. Long-term observations (1960--2020) show that most of the rainy days in the hyperarid core (75\%) are triggered by MNs. A trough over the southeast Pacific and a southward displaced Bolivian High dynamically drives them, occurring more frequently during the neutral-cold phase of El Niño-Southern Oscillation (ENSO) and phases 7-8-1 of the Madden-Julian Oscillation (MJO). A trend analysis (1991--2020) reveals that summer water vapor along the subtropical west coast of South America has increased rapidly due to the MNs, enhancing summer rainfall in the Atacama. The implications of climate change and other variability modes are discussed.