In the open ocean, floating surface debris such as plastics concentrate in five main accumulation zones centered around 30° latitude, far from highly turbulent areas. Using Lagrangian advection of numerical particles by surface currents from ocean model reanalysis, previous studies have shown long-distance connection from the accumulation zones of the South Indian to the South Pacific oceans. An important physical process affecting surface particles but missing in such analyses is wave-induced Stokes drift. Taking into account surface Stokes drift from a wave model reanalysis radically changes the fate of South Indian particles. The convergence region moves from the east to the west of the basin, so particles leak to the South Atlantic rather than the South Pacific. Stokes drift changes the South Indian sensitive balance between Ekman convergence and turbulent diffusion processes, inducing either westward entrainment in the north of the accumulation zone, or eastward entrainment in the south.