It’s even cooler than that: The esophagus can squeeze things towards the stomach against gravity. You can drink water while hanging upside down. You’ll also get a nose full of water because your sinuses would be below your mouth… But once it’s in your throat and you’re swallowing, it’ll make it to your stomach just fine.

If you wanted to avoid the sinus problem, I guess you could just lay on your back on a steep incline. Not fully upside down, so your sinus cavity is still above your mouth. That way the water would hit the back of your throat where you could swallow it, instead of just draining straight into your sinuses.