Mammalian cell invasion by the protozoan parasite Trypanosoma cruzi involves host cell microtubule dynamics. Microtubules support kinesin-dependent anterograde trafficking of host lysosomes to the cell periphery where targeted lysosome exocytosis elicits remodelling of the plasma membrane and parasite invasion. Here, a novel role for microtubule plus-end tracking proteins (+TIPs) in the co-ordination of T. cruzi trypomastigote internalization and post-entry events is reported. Acute silencing of CLASP1, a +TIP that participates in microtubule stabilization at the cell periphery, impairs trypomastigote internalization without diminishing the capacity for calcium-regulated lysosome exocytosis. Subsequent fusion of the T. cruzi vacuole with host lysosomes and its juxtanuclear positioning are also delayed in CLASP1-depleted cells. These post-entry phenotypes correlate with a generalized impairment of minus-end directed transport of lysosomes in CLASP1 knock-down cells and mimic the effects of dynactin disruption. Consistent with GSK3β acting as a negative regulator of CLASP function, inhibition of GSK3β activity enhances T. cruzi entry in a CLASP1-dependent manner and expression of constitutively active GSK3β dampens infection. This study provides novel molecular insights into the T. cruzi infection process, emphasizing functional links between parasite-elicited signalling, host microtubule plus-end tracking proteins and dynein-based retrograde transport. Highlighted in this work is a previously unrecognized role for CLASPs in dynamic lysosome positioning, an important aspect of the nutrient sensing response in mammalian cells.