Dragonflies perform dramatic aerial manoeuvres when hunting prey or chasing rivals but glide leisurely with wings virtually fixed. This makes dragonflies a great system to explore how to minimize the trade-off between manoeuvrability and stability. We challenged the dragonfly by dropping it from selected inverted attitudes and digitised the 6-degrees-of-freedom aerial recovery kinematics via custom motion capture techniques. From these kinematic data we then performed rigid-body inverse dynamics to reconstruct the forces and torques involved in the righting behaviour. We found that inverted dragonflies typically recover themselves with the shortest rotation from the initial body inclination. Additionally, they exhibited a strong tendency to pitch up with their head leading out of the manoeuvre. Surprisingly, anaesthetised dragonflies could also complete the aerial righting. Such passive righting disappears in recently dead dragonflies but can be partially recovered by waxing their wings to mimic the wing posture of the anesthetised dragonflies. Our inverse dynamics model and wind tunnel experiments support the idea that certain wing postures readily provide stability and may explain the dragonfly’s rotational preference. This work demonstrates for the first time that aerodynamically stable body configuration exists in gliding insects, and an active insect can leverage this passive stability as needed.