There are no doubt other ways to do it, and this worked on my machine, so YMMV.
First, go here and download the driver packs. I think you only need the Surface Pro 3 zip file, but I downloaded all of them for the hell of it.
Next, uninstall your wireless driver from Device Manager, choosing to delete it from your machine.
Then, unzip the zip file (making sure to unblock it, if needed by right-clicking, choosing properties, and choosing unblock).
Then, in device manager, you should have an unidentified network adapter/ethernet controller/whatever, so right-click it, choose to install a driver for it, manually navigate to the unzipped directory, and install it.
You should be good to go, though you will need to reenter your network key when you reconnect to your wireless network.