If I sell a rental that was my primary residence until 10/1/18, must I complete the sale by 10/1/21 to claim a capital gains exemption? Close escrow on sale by then?

for the home sale exclusion, you have to use the property as your primary residence for 730 days in the 5 years before the sale. the 730 days do not have to be consecutive.

Q. Must I complete the sale (date of closing) by 10/1/21 to claim a capital gains exemption? 

A. Yes. That's how it works.  Make it 9/30/21, just to be sure. 

You will not have to allocate any of the gain to rental time, but will have to pay tax on  the depreciation recapture.