By conducting three-dimensional hydrodynamical simulations we find that jets that a main-sequence companion launches as it orbits inside the wind acceleration zone of an asymptotic giant branch star can efficiently remove mass from that zone. We assume that during the intensive wind phase a large fraction of the gas in the acceleration zone does not reach the escape velocity. Therefore, in the numerical simulations we blow the wind with a velocity just below the escape velocity. We assume that a main-sequence companion accretes mass from the slow wind via an accretion disk, and launches two opposite jets perpendicular to the equatorial plane. This novel flow interaction shows that, by launching jets, a companion outside a giant star, but close enough to be in the acceleration zone of a slow intensive wind, can enhance the mass-loss rate from the giant star by ejecting some gas that would otherwise fall back onto the giant star. The jets are bent inside the wind acceleration zone and eject mass in a belt on the two sides of the equatorial plane. The jet-wind interaction contains instabilities that mix the shocked jets' gas with the wind, leading to energy transfer from the jets to the wind. Our new simulations add to the rich variety of jet-induced outflow morphologies from evolved stars.