Now everything is back to normal.
I ran the virus scan after the first time, and it ran itself yesterday, finding nothing.
I actually started to phone the number on the bogus MS support site but stopped and googled it.
Lots of threads about how to stop the "annoying ***-***-**** pop-up" but when I clicked on any of them, nothing happened. Definitely seems like a browser takeover, as ITHRN suggests.
Anyway, don't click any of my links!
Thanks for all the comments.