We address stabilization of vectored-thrust Unmanned Aerial Vehicles (UAVs): a challenging task due to the peculiar nonlinear underactuated dynamics. According to a wellestablished approach based on the selection of suitable error variables, the error dynamics is described as a pseudo cascade connection where the attitude subsystem indirectly stabilizes the position dynamics. Unlike existing works, we address stability of this cascade using integral Input to State Stability (iISS). With this extension it is possible to employ a quasi time-optimal control law to achieve global asymptotic stabilization of any desired position, thus improving the transient performance with respect to existing control designs. A simulation example shows the performance improvement in comparison with a nested saturations stabilizer.