Yup, as noted by Reddit users xharry998, you can play PS3 games using the DualSense controller by connecting it to your console via the Brook Wingman XE.

Here's how to connect a DualShock 4 controller to a PS3 and get it to run wirelessly.

If you are having difficulty starting your PlayStation 3, you may need to start it in recovery mode. This FAQ will show you how to get started and access recovery mode.

Step 1: Get MotionInJoy The PS3 controller did not seem to come with its native drivers, and the only way to make it work with my computer was with the MotionInJoy Application.