Mitochondria are essential organelles in eukaryotic cells, enclosed by two membranes with distinct compositions and functions. In addition to the endoplasmic reticulum, mitochondria are major sites of cellular lipids production. Cardiolipin, for example, is exclusively synthesized in the mitochondrial inner membrane. This requires the precursor lipid phosphatidic acid to be imported from the endoplasmic reticulum to the mitochondrial outer membrane. Subsequently phosphatidic acid is transferred to the inner membrane by the lipid transfer protein Ups1/PRELID1. The regulation of this process, the role of membrane physico-chemical properties, and the mechanisms by which energy barriers are overcome during lipid extraction and insertion remain poorly understood. Here, we demonstrate that Ups1 exhibits a strong preference for binding to positively curved membrane regions. Our findings reveal that phosphatidic acid extraction is energetically favored at these membrane domains, leading to enhanced lipid transfer between membranes with high positive curvature. We further show, that lipid extraction is the rate-limiting step in the transfer cycle. Our data suggest that Ups1 membrane binding is modulated by pH, lipid composition, and membrane morphology, pointing to a complex, multipartite regulatory network underlying intra-mitochondrial lipid transfer.