If the Chiefs are supposed to play in your market (mine was NYC on Sunday) but CBS / FOX switches "to a more competitive game", try the NFL App.
I've found that the NFL app will still let you see it, if the game was indeed supposed to play in your market,
On Sunday, this worked for me both at the beginning (when Bengals/Steelers preempted the first quarter), and at the end (when they went to Raiders-Chargers).
This worked for me on at least one occasion last year too--which is when I discovered this nice trick.
Note: on Sunday it worked for my iPad and iPhone, but my AppleTV NFL app didn't let me do it. Not sure why. I haven't tried Android or a PC.
Hopefully this is a situation that happens to us again (with us in the lead of course!) and this is helpful!