Bochy's men were looking down the barrel of a 3-1 series deficit to fellow post-season wildcards the Kansas City Royals, as they trailed Saturday's encounter 4-1 midway through the third inning.
But some stunning Giants offense and defense saw them eventually canter to an 11-4 win to square the MLB's championship series at 2-2.
Of the 12 players to have an at-bat for the National League champions, 11 had base hits - with Hunter Pence (three) leading the way while Pablo Sandoval, Joe Panik and Gregor Blanco also had multiple hits.
"You hear the term 'team win'," Bochy said.
"It's used quite a bit, but if you look at that game, everybody did something to contribute, from the bullpen to the hitters, pinch-hitters, [Matt] Duffy, big hit, he scores. [Joaquin] Arias [too].
"All these little things added up for us mounting that comeback, a great comeback."
Bochy said his side's ability to scratch their way to victory having been hit-less heading to the bottom of the third with a 4-1 deficit was extraordinary.
"It's obvious we think it's a great game. These guys fought hard. I mean, they scratched and clawed to get back in it," Bochy said.
"You know, you get down against this club [the Royals] and that bullpen, you have your work cut out. But these guys didn't stop fighting."
Sandoval, who hit the go-ahead two-run single, conceded he was feeling ill 24 hours from game four, but got himself up for the clutch base hit for his team-mates.
"I didn't feel great yesterday," Sandoval said post-match.
"As I said it was a tough moment to be sitting on the bench, I just told myself you have to go out and play with aspiration ... I just tried to tell myself, 'You're the guy. Step up for your team-mates. You try and get a base hit out there and score two runs'."
Sandoval said the Giants were buoyed by the fans, who are spurring on their team for a third World Series win in five years.
In even better news for San Francisco, star pitcher Madison Bumgarner is set to start game five - and is poised to give the Giants a series lead heading to game six in Kansas City.
"It is a big difference to win. Tomorrow [Sunday] there's going to be another game," Sandoval said.
"We're going to play hard for the fans, they enjoyed this moment.
"Tomorrow is going to be important for us, we're going to have Madi back on the mound so we're going to do the best we can."
Meanwhile, Kansas City Royals manager Ned Yost was refusing to be downbeat after seeing his men hauled back in the series.
He even insisted he was hoping the battle for baseball's showpiece would go down to the wire, anticipating the drama of a potential seventh game.
"I always feel good with this group," he said. "They've been playing great baseball.
"We have got a really tough challenge tomorrow with Bumgarner [returning].
"We got our tails whipped today, but it's game four of the World Series. We're tied 2 2, how much more fun can that be?
"There is nothing better in the world. I've never felt so good about getting my tail whooped in my life, because I'm sitting here thinking 'It's game four. It's tied 2-2. This is a phenomenal series. It's exciting. It's fun, and we've got another great game tomorrow that we get to play'. So [I'm] really looking forward to it.
"Oh, man, somewhere inside of me secretly I had hoped that it would go seven games for the excitement and the thrill of it. Sure looks that way."