Turning off the computer screen without pressing the Power button on the monitor is possible with PushMonitOff, a program that enables a keyboard shortcut for this purpose. So every time you press the Shift + F1 keys the monitor will turn off whether it is a PC or a laptop, allowing you to do it through the system tray as well.
Thanks to PushMonitOff you no longer have to physically touch the monitor to turn it off and you can even do it with a laptop screen. Pressing the Shift and F1 keys at the same time, the monitor will switch off immediately. If you prefer to do it with another keyboard shortcut just define it by choosing the keys you want.
If you want to turn off the screen with the mouse, you can do so by accessing the PushMonitOff icon in the system tray and selecting the relevant option.