Android - How to power-off Motorola phone without screen

I can't be sure that this is the optimal way to power-off the phone, but it seems to work.

1. Press and hold power until it buzzes or about 15 seconds, then release.
2. Press and hold volume-down and the power button for 20 seconds, then release.
3. Press and release the power button once.

This procedure is demonstrated in a you tube video https://youtu.be/x_jx5u7dXK4

Tip: Even though the broken phone has no display functionality, if you view the phone with another camera, you can check activity of this phone by looking at the infrared emitters at the four corners of the device. Before power-down, these dots will be flickering. Afterwards, no flickering.

Came upon this when I was looking for a way to shut down my Moto Z with a broken screen and the method described by Dale (thank you) almost worked, but then I figured out it required one extra step. I probably won't be the only one in this predicament, so allow me to contribute. The procedure described above works by opening the fastboot menu and selecting the "power off" option using the power button. Problem is it would seem newer phones have "start" as the default option instead of "power off". The solution is simply to scroll down to "power off" by pressing the volume down key THREE TIMES and then push the power button.

In summary, to shut the phone down without being able to see what's on screen:

1. Hold power button for about 15 seconds until it vibrates. This will initiate a restart.
2. While phone is restarting, hold both the power and volume down button for 20 seconds. This will make the phone load up the fastboot menu.
3. (For Moto Z, Z2, and probably other models. For Moto X, skip this step) Press the volume down button exactly three times. This should scroll it down to "power off".
4. Press power button to select "power off".

As mentioned before, if you're unsure if the phone's off or not, you can check the infrared emitters for glowing using another camera. Hope this helps anyone else who comes across here.