We present a new magnetic map integrating continental and oceanic features at Santos Basin, in order to investigate the connection between onshore and offshore tectonics and magmatism at the early stages of rifting. The magnetic and seismic data evidence the offshore continuity of the Florianópolis and Serra do Mar dyke swarms while the Ponta Grossa Dyke Swarm was discontinued by the marginal structures. This brings to evidence a different timing of formation of the latter relative to the early opening of the margin. A very high amplitude magnetic lineament - the Santos Marginal Anomaly (SAMA) reaches up to 1500 nT and trend NE-SW, with local E-W inflections forming the Cananéia and Guaratiba Arcuate Anomalies. Our modeling suggests that SAMA can be associated with dykes and syn-rift extrusives linked at depth to larger magmatic bodies at the proximal and necking domains. Based on the increasing width and amplitude of the magnetic anomalies oceanwards, we propose a mechanism where the igneous accretion augmented as rifting evolved from continent to ocean, creating a volcanic rift axis. This rift was segmented by crustal discontinuities that probably nucleated on preexisting rheological contrasts, forming tectono-magmatic segments during the early extensional stages. The onshore-offshore relationships highlight that where there was an agreement between basement fabric and dyke orientation, inheritance may have influenced their emplacement, although it was not a limiting factor for their formation. The regional geodynamics of the Gondwana opening was the first order control, with deviations of the magmatically influenced rift by inheritance.