When users in virtual reality cannot physically walk and self-motions are instead only visually simulated, spatial updating is often impaired. In this paper, we report on a study that investigated if HeadJoystick, an embodied leaning-based flying interface, could improve performance in a 3D navigational search task that relies on maintaining situational awareness and spatial updating in VR. We compared it to Gamepad, a standard flying interface. For both interfaces, participants were seated on a swivel chair and controlled simulated rotations by physically rotating. They either leaned (forward/backward, right/left, up/down) or used the Gamepad thumbsticks for simulated translation. In a gamified 3D navigational search task, participants had to find eight balls within 5 min. Those balls were hidden amongst 16 randomly positioned boxes in a dark environment devoid of any landmarks. Compared to the Gamepad, participants collected more balls using the HeadJoystick. It also minimized the distance travelled, motion sickness, and mental task demand. Moreover, the HeadJoystick was rated better in terms of ease of use, controllability, learnability, overall usability, and self-motion perception. However, participants rated HeadJoystick could be more physically fatiguing after a long use. Overall, participants felt more engaged with HeadJoystick, enjoyed it more, and preferred it. Together, this provides evidence that leaning-based interfaces like HeadJoystick can provide an affordable and effective alternative for flying in VR and potentially telepresence drones.