The interaction between magmatism and sedimentation creates a range of petroleum plays at different stratigraphic levels due to the emplacement and burial of volcanoes. This study characterizes the spatio-temporal distribution of the fundamental building blocks (i.e., architectural elements) of a buried volcano and enclosing sedimentary strata to provide insights for hydrocarbon exploration in volcanic systems. We use a large data set of wells and seismic reflection surveys from the offshore Taranaki Basin, New Zealand, compared with outcropping volcanic systems worldwide to demonstrate the local impacts of magmatism on the evolution of the host sedimentary basin and petroleum system. We discover the architecture of Kora volcano, a Miocene andesitic polygenetic stratovolcano that is currently buried by more than 1000 m of sedimentary strata and hosts a subcommercial discovery within volcanogenic deposits. The 22 individual architectural elements have been characterized within three main stratigraphic sequences of the Kora volcanic system. These sequences are referred to as premagmatic (predate magmatism), synmagmatic (defined by the occurrence of intrusive, eruptive, and sedimentary architectural elements), and postmagmatic (degradation and burial of the volcanic structures after magmatism ceased). Potential petroleum plays were identified based on the distribution of the architectural elements and on the geologic circumstances resulting from the interaction between magmatism and sedimentation. At the endogenous level, emplacement of magma forms structural traps, such as drag folds and strata jacked up above intrusions. At the exogenous level, syneruptive, intereruptive, and postmagmatic processes mainly form stratigraphic and paleogeomorphic traps, such as interbedded volcano-sedimentary deposits, and upturned pinchout of volcanogenic and nonvolcanogenic coarse-grained deposits onto the volcanic edifice. Potential reservoirs are located at systematic vertical and lateral distances from eruptive centers. We have determined that identifying the architectural elements of buried volcanoes is necessary for building predictive models and for derisking hydrocarbon exploration in sedimentary basins affected by magmatism.