High vein density (DV) evolution in angiosperms represented a key functional transition. Yet, a mechanistic account on how this hydraulic transformation evolved remains lacking. We demonstrate that a consequence of producing high DV is that veins must become very small to fit inside the leaf, and that angiosperms are the only clade that evolved the specific type of vessel required to yield sufficiently conductive miniature leaf veins. From 111 species spanning key divergences in vascular plant evolution, we show, using analyses of vein conduit evolution in relation to vein packing, that a key xylem innovation associated with high DV evolution is a strong reduction in vein thickness and simplification of the perforation plates of primary xylem vessels. Simple perforation plates in the leaf xylem occurred only in derived angiosperm clades exhibiting high DV (> 12 mm mm⁻²). Perforation plates in the vessels of other species, including extant basal angiosperms, consisted of resistive scalariform types that were associated with thicker veins and much lower DV. We conclude that a reduction in within‐vein conduit resistance allowed vein size to decrease. We suggest that this adaptation may have been a critical evolutionary step that enabled dramatic DV elaboration in angiosperms.