You can't really talk about great post-season pitching performances without mentioning Koufax. In 63, he started two games, and finished them both, giving up a total of 3 earned runs, and striking out 23, giving up 12 hits and 3 walks. In 65, he was even better. He pitched 3 games in the WS, went 24 innings, struck out 29, walked 5, gave up 13 hits and ONE earned run.
Totally different time back then, with so many less post-season games, but he has to be mentioned.
Likewise, in 67, a guy named Bob Gibson threw 3 complete games in the world series, striking out 26, walking 5 and giving up 14 hits and 3 earned runs. He followed that up the following year with 3 more complete games in the world series, striking out 35 in 27 innings, walked 4, gave up 18 hits and 5 earned runs.
Oh yeah, Gibson also threw 2 complete games in the 64 world series (he pitched 27 innings, but one game went extras that he didn't finish) and struck out 31 that year. In 3 series, he pitched 9 games, 81 innings. Basically, him and Koufax did what Bumgarner did in the world series every year for about 5 straight years.