It isn't possible to change the power status of a USB port from User mode code. It's not a .NET limitation, no user application can change the power status of a USB port. Actually, I think that the power state is controlled by the chipset itself and you can't turn it off without using a specialized chipset.
Besides, if your device short-circuited, you could burn your chipset and your motherboard.
The only (safe) solution is to use an external device that will control a relay to turn power on or off for your devices.
There are multiple answers to similar questions, eg Windows- Power off a USB device in Software
A good option is to use an external device like Arduino (or Netduino), .NET Gadgeteer or any number of external boards. Prices and capabilities vary of course.
If you want to build the device yourself, you can find numerous USB relays with a simple Google search
EDIT
Regarding serial ports, there is almost no relation at all between the two port types. Serial ports are not designed to provide power. You can use tricks to use a pin's voltage to power some external device, although this will lead to problems because there is not enough current to power most devices. Burning the chipset is another likely outcome.
A USB port on the other hand, is explicitly designed to provide power through specific wires which can't be controlled normally. This is why you can charge your phone from a desktop's USB port even if the machine has shut down.
EDIT 2: Sleep-and-charge ports
As Ben Voigt noted, not all USB ports allow charging while shutdown.
There are multiple port types that support charging. Charging ports provide more current than plain ports but shut down when the computer is switched off. Sleep-and-charge ports on the other hand can provide power even when the computer is off.