With Hope scoring 101 in just his second ODI, the West Indies were well on track to overhaul Zimbabwe's 257 as they went into the final six overs on 217 for two.
But Hope's dismissal sparked a late collapse, which included three wickets in the final over.
The tourists needed just four runs off Donald Tiripano's last over with five wickets in hand, but instead finished on 257 for eight to share the points.