1971 Greenville 200 was broadcast live flag to flag during ABC's Wide World of Sports Block. The network occasionally showed partial races (including the entire second halves of 1970 races from North Wilkesboro and Talladega), but Greenville was the first time they went flag to flag. https://www.youtube.com/watch?v=LueNWi3Gdj0
ABC basically got out of the NASCAR business after the series changed formats and Winston took over sponsorship except for the Daytona 500, and starting in '79 they lost that to CBS.
The second race broadcast to TV in it's entirety that exists is the 1979 Daytona 500, also available in full via an official upload from NASCAR: https://www.youtube.com/watch?v=-K-GkXe70Vk
Between the two, for the 1978 World 600, full video was recorded and preserved (albeit in lower quality) with nat. sound from the track. This is not an official broadcast, however https://www.youtube.com/watch?v=L3tuXDbQu7g
Other mentioned partial races in this post: 1970 Darlington 400: https://www.youtube.com/watch?v=7NAdZp-zVJ8 1970 North Wilkesboro 2nd Half: https://www.youtube.com/watch?v=JaF1dXE4AEU 1970 Talladega 2nd Half: https://www.youtube.com/watch?v=uzb7nWyjwBU 1976 Daytona 500 (start, lookins, epic finish): https://www.youtube.com/watch?v=WUSECWVO2Js