Brandon Crawford gave Bumgarner more than enough run support with the third grand slam of his career in the fourth inning and first by a shortstop in post-season history.
"That's crazy," Crawford said. "With all the great shortstops that have played before, that's pretty special. I'm happy to be able to do it."
Bumgarner, Crawford and their teammates have advanced to the NL Division Series against Washington, a best-of-five set that starts Friday.
Bumgarner, fresh off an 18-win season and 2.98 ERA over 33 starts, was sensational from start to finish on Wednesday, not allowing a runner past second base until the eighth inning when errors by third baseman Joaquin Arias and Crawford allowed Jose Tabata to reach third.
Bumgarner ended the threat by fanning Jordy Mercer and inducing Andrew McCutchen to ground out to short.
In the ninth inning, he retired catcher Russell Martin of Montreal, outfielder Starling Marte and second baseman Neil Walker for his fourth career post-season victory.
"It's fun," Bumgarner said. "If you're not playing, you can be excited and nervous and all that. But if you're pitching in the game you've got to try to push that all aside and try to make pitches like we did tonight."
Giants first baseman Brandon Belt, who had concussion problems late in the season, drove in three runs on a pair of hits while catcher Buster Posey knocked in the other run during a two-hit night.
Meanwhile, a recent managerial decision might haunt Pittsburgh's Clint Hurdle for at least a portion of the off-season.
Prior to Sunday’s first pitch at Cincinnati, his Pirates had already, at worst, clinched a spot in the NL wild-card game.
But there was still a chance Pittsburgh could force a division tiebreaker for the Central Division crown with St. Louis, so Hurdle elected to start 24-year-old fireballer Gerrit Cole, some would say the Pirates best starting pitcher, rather save him for the win-or-go-home wild-card contest.
Well, the Reds beat the Pirates 4-1 despite a stellar seven-inning effort by Cole, who limited his opponent to a run on four hits and struck out 12. And St. Louis blanked Arizona 1-0 to maintain its lead and win the division.
So, Hurdle turned to second-half standout Edinson Volquez Wednesday against San Francisco after he posted a 5-0 record and 1.78 ERA over his final 12 starts of the regular season, losing only once after the all-star break.
Volquez made Hurdle look like a genius early on, allowing a couple of singles through the first three innings and seemingly prepared to turn in another of his recent gems on the mound.
That would be far better than the hurler’s only previous post-season start while a member of the Reds. In Game 1 of the 2010 NL Division Series, Volquez lasted just 1 2/3 innings against Philadelphia after coughing up four runs.
However, once the Giants got a second look at the 32-year-old Volquez in the top of the fourth inning, Hurdle might have started second-guessing himself. Three batters later, the bases were loaded following back-to-back singles by Pablo Sandoval and Hunter Pence and a walk to Belt.
Crawford, who had lined out to right field in the second, didn’t miss this time, turning on a Volquez breaking ball for his 11th homer of the season.
Crawford's grand slam was the fourth in Giants post-season history.
"The last thing on my mind was probably hitting a home run," Crawford said. "I was just trying to hit something good enough to get Pablo home, and I figured that would probably be good enough for Madison."
Shortstop had been the only position, including pitcher, without a slam in post-season play.
Giants: OF Michael Morse was left off the wild-card roster while he recovers from a strained oblique that has sidelined him since Sept. 20. Manager Bruce Bochy said the veteran would be activated "at some point" in the next round.
"It would be nice to have him coming off the bench, but he's not quite ready," Bochy said.
It's on to Washington for the Giants, where they will face rookie manager Matt Williams and the Nationals. Williams was once a star third baseman for San Francisco.
The Giants went 2-5 against Washington this season, getting outscored 41-30.