TK-41 1967 MN Twins at Boston Red Sox
 

Haven't looked around enough to verify if this tape is indeed "the oldest complete telecast of a major league baseball game in color," there is some footage of a 1965-08-19 Cincinnati Reds at Chicago Cubs game floating around on YouTube, but not sure if the complete footage for that game exists. In any case, here is some "extended" TK-41 footage from 1967 of the Minnesota Twins at the Boston Red Sox.

https://www.youtube.com/watch?v=Cze3fMSa84w