The parasitic plant Striga hermonthica invades the host root through the formation of a haustorium and has detrimental impacts on cereal crops. The haustorium is derived directly from the differentiation of the Striga radicle. Currently, how Striga root cell lineages are patterned and the molecular mechanisms leading to radicle differentiation shortly after germination remain unclear. In this study, we determined the developmental-morphodynamic programs that regulate terminal haustorium formation in S. hermonthica at spatiotemporal and cellular resolutions. We showed that in S. hermonthica roots, meristematic cells first undergo multiplanar divisions, which decrease during growth and correlate with reduced expression of the stem cell regulator PLETHORA1. We also found that PIN-FORMED (PIN) proteins undergo a shift in polarity. Using the layout of the root structure and the polarity of outer-membrane PIN proteins, we constructed a mathematical model of auxin transport that explains the auxin distribution patterns observed during S. hermonthica root growth. Our results reveal a fundamental molecular and cellular framework governing the switch of S. hermonthica roots from the vegetative to the invasive state by inducing meristem differentiation through auxin excretion to the environment and explain how asymmetric PIN polarity controls auxin distribution to maintain meristem activity and sustain root growth.