Xbox one controller rechargeable battery
Yes, you can use a 14500 lithium ion battery (nomial 3.6V) and use a regulator for reducing the voltage to 3.0V. But then the 0.6V voltage drop (times current) is just "burned" in the regulator, which means this is not very efficient. For better efficiency, you could use a switching DC/DC converter which converts the input voltage to a fixed output voltage (say 2.7V) without loosing too much energy. (Using a zener diode does not make sense in your context.)