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Discrete structures (e.g. faults) or pervasive fabrics (e.g. foliation), which may occur in pre-rift sedimentary and/or crystalline basement rock, can control the growth and geometry of rift-related normal fault arrays. Previous studies examining how such structures/fabrics affect rift geometry typically rely only on plan-view correlations between the strike and dip of observed or, in some cases, inferred pre- and syn-kinematic structures. Three-dimensional relationships between and kinematic evolution of, pre-existing structures/fabrics and rift-related normal faults remains poorly constrained because: (i) outcrop patterns rarely expose both rift-related normal faults and the underlying rock units that could host pre-kinematic structures; (ii) discrete structures or pervasive fabrics are often poorly imaged in seismic reflection data; and (iii) it is difficult to quantitatively assess how pre-kinematic structures/fabrics influence normal fault nucleation and growth. Here, we use 3D seismic reflection data from the Taranaki Basin, offshore western New Zealand to study the kinematic history of a Cenozoic, rift-related, NE-SW striking normal fault array developed above a suite of N-S striking, intra-basement reflections interpreted as Palaeozoic thrusts. Only six of the 16 mapped rift-related normal faults mirror the strike of and appear physically linked to, the basement thrusts for at least 50% of their strike length; this spatial relationship would typically be inferred to reflect reactivation and upward propagation of the basement thrusts during rifting. However, fault throw analysis reveals the normal faults nucleated in the sedimentary cover ~1–2 km above the unconformity marking the top basement. We show the rift-related normal faults propagated downwards to either intersect NE-SW striking thrust segments or twisted to become aligned with the local strike of the basement structures. We propose that the presence and subtle reactivation of basement thrusts during Cenozoic extension locally reoriented the principal stress axes within the sedimentary basin, causing rift-related normal faults to deviate from their dominant NE strike. Despite having superficially similar strikes, rift-related normal faults may not simply form due to reactivation and upward propagation of basement structures.