Bumgarner pitched seven strong innings and Buster Posey went 4-for-4 with his 14th homer as the Giants topped the Cubs for a 5-3 victory Thursday night.
"He's as mentally tough as you get," Giants manager Bruce Bochy said of his young pitcher. "He's got a knack for making pitches when he has to."
Bumgarner (14-9) struck out 12 in seven innings. He allowed three runs and seven hits.
He finished his strong outing by striking out touted Cubs prospect Javier Baez with two out and two runners in scoring position in the seventh.
"It was a really gutty effort that last inning," Bochy said. "He's our guy, and he got a big strikeout there."
Baez struck out four times on the night. Through 71 big league at-bats, he has struck out 31 times.
The long day started with a rain delay of 1 hour, 57 minutes, and then the Cubs and Giants played the final 4½ innings of a game the Cubs thought they had won 2-0 on Tuesday night.
A short rainstorm caused a delay of more than 4½ hours after the grounds crew struggled with the tarp. The umpires said the field was unplayable and called it at 1:16 a.m. local time.
But the Giants protested, and Major League Baseball ruled that the tarp had not been properly put away after its previous use. The game was ruled suspended.
"It was a little bit of a strange one with the suspended game today," said Bochy, who heavily criticized the initial ruling Tuesday night. "You know, they got it right."
It was the first successful protest in MLB since 1986.
Anthony Rizzo's two-run homer from Tuesday held up for Chicago in the early game. Joe Panik had an RBI single in the sixth to pull the Giants to 2-1, but Pedro Strop worked the eighth and Hector Rondon picked up his 19th save in 23 opportunities.
"It's been a long three days," Cubs manager Rick Renteria said of the series. "I wished we could have finished it off the second game in our favor, but obviously we didn't."
Wood (7-11) gave up four runs and eight hits in six innings. The left-hander is 0-6 with a 5.45 ERA in his past 12 starts.
Santiago Casilla worked a scoreless ninth for his 11th save in 14 opportunities.
Cubs: Right-hander Edwin Jackson was placed on the 15-day disabled list with a right lat strain. Jackson dealt with a similar injury at the end of last season and hopes that by going on the DL now, he will be able to pitch again in September. ... Shortstop Starlin Castro was placed on the bereavement list after leaving the team for a family emergency.
Giants: Infielder Ehire Adrianza has been slow to recover from a second strained groin injury, which raises doubts about his status in the final weeks of the season. "He's not ready yet, so that's another decision we'll have to make," Bochy said. ... Bochy was optimistic that first baseman Brandon Belt and catcher Hector Sanchez would recover from concussions in time for the stretch drive.