Some evolved stars in the pre-planetary nebula phase produce highly collimated molecular outflows that resemble the accretion-driven jets and outflows from pre-main-sequence stars. We show that IRAS 16342−3814 (the Water Fountain Nebula) is such an object and present K-band integral field spectroscopy revealing a fast (>150 km s−1) bipolar H2 outflow. The H2 emission is shock excited and may arise in fast-moving clumps, accelerated by the previously observed precessing jet. The total luminosity in H2 is 0.37 L⊙, which is comparable with that of accretion-powered outflows from Class 0 protostars. We also detect CO overtone bandhead emission in the scattered continuum, indicating hot molecular gas close to the centre, a feature also observed in a number of protostars with active jets. It seems likely that the jet and outflow in IRAS 16342−3814 are powered by accretion on to a binary companion.