Several ODP-IODP expeditions drilled oceanic core complexes interpreted as exhumed portions of lower crust close to the ridge axis, and provide the community with invaluable sampling opportunity for further constraining magmatic processes involved in the formation of the slow-spreading lower oceanic crust. ODP Hole 735B presents the most primitive lithologies sampled at Atlantis Bank oceanic core complex (Southwest Indian Ridge) in a ∼250 m thick section that was previously interpreted as a single crustal intrusion. We combined detailed structural and petrographic constraints with whole rock and in situ mineral analyses of this section in order to precisely determine the processes of emplacement, crystallization, and melt migration within the lower crust. The lower half of the unit is comprised of alternating olivine gabbros and troctolites showing intrusive contacts, magmatic fabrics, and crystal-plastic fabrics. Such structures and primitive lithologies are lacking in the upper half, rather uniform, gabbroic sequence. Whole rock compositions highlight the cumulative character of both lower and upper units and a great compositional variability in the lower sequence, whereas the upper sequence is homogeneous and differentiates up-section. In situ analyses of mineral phases document magma emplacement processes and provide evidence for ubiquitous reactive porous flow (RPF) during differentiation. We show that the whole section, and related geochemical unit, constitutes a single magmatic reservoir, in which the lower unit is formed by stacked primitive sills formed by repeated recharge of primitive melts and melt-present deformation. Recharge led to partial assimilation of the crystallizing primitive cumulates, and hybridization with their interstitial melts. Hybrid melts were progressively collected in the overlying mushy part of the reservoir (upper unit), whereas the sills’ residual hybrid melts differentiated by RPF processes under a predominantly crystallization regime. Similarly, hybrid melts’ evolution in the upper unit was governed by upward RPF, and progressive differentiation and accumulation of evolved melts at the top of the reservoir. Our results provide the community with the first integrated model for magma reservoir formation in the lower slow-spreading oceanic crust that can potentially be applied to other magmatic lower crust sections.