I have a powered USB hub. Can I use it to power the Raspberry Pi Zero using up just one Micro USB port? Or does the power have to come from one particular port that is only used to provide power?
The Pi zero has only one USB port. It has two microUSB sockets.
The socket closer to the edge of the long side of the board is the power socket. The socket closer to the middle of the long side of the board is a USB port.
You seem to be able to back power via the USB port. You will have to judge the reliability of back powering the Pi zero by personal experience.
Assuming the micro-USB socket "power" of the Pi Zero is used to power the Pi, I take it that the question refers to the USB ports or sockets of the used hub as a source. Further assuming that we're talking about a self-powered hub here, as a bus-powered hub cannot supply more than 500 mA in total to its downstream ports. So according to USB spec a USB port should provide 100 mA per default and 500 mA after annoucement of the device to the hub/host (USB 1.x and 2.0), and 900 mA (USB 3.x).
In real life most hubs out there don't care much about those limits. Typically their ports supply more than 500 mA. We can now call that non-compliant devices or embrace the fact to power the Pi.
I've used both a Pi B+ and a Pi 2 with a USB 2.0 hub and a simple wiring: USB downstream port to the Pi's micro-USB power socket. Works just fine. Given the available technical data on the Pi Zero, it's safe to assume it would not consume more power than a Pi 2.
Bottom line: assuming a "reasonably non-compliant" USB hub it will probably just work.