I am pretty sure you can find one maybe two complete games from the 1952 World Series between the NY Yankees and Brooklyn Dodgers on YouTube. But finding earlier complete games might be hard to find. You should however be able to find some complete games from the 80s and 90s and maybe even the 70s. Also iTunes should have complete games from the 70s to the modern era. They shouldn't be too expensive, a few $$$ each. But it will cost you money and these days we need to be smart with our spending.
So my recommendation is to search YouTube. Also a lot of Super Bowl games (maybe not all of them, but many of them) can be found on the NFL's YouTube channel if you also want to watch some football.