Bumgarner, a rookie left-hander, dominated baseball's top-hitting team from the start, allowing only three hits, walking two and striking out six as the Giants took a commanding 3-games-to-1 lead over the Rangers in the 2010 Fall Classic.
Bumgarner (1-0) allowed only one runner to reach as far as second base, and at age 21 became the fourth-youngest pitcher to ever start and win a World Series game.
Brian Wilson pitched a 1-2-3 ninth to complete the shutout.
Huff broke a scoreless tie in the third inning with a long, two-run homer off Rangers starter Tommy Hunter (0-1). Buster Posey added a solo shot and Andres Torres drove in San Francisco's other run.
Hunter went four innings for Texas, allowing a pair of runs on five hits, walking one and striking out one.
The Rangers will try to avoid a World Series defeat in Monday's Game 5 when they send ace left-hander Cliff Lee to the mound to face his opponent in Game 1, San Francisco's Tim Lincecum.