Greinke, who lasted 7 1/3 innings, is 15-3 with a 1.59 ERA of historic proportion. Bumgarner, yielding both runs across seven innings, slipped to 16-7.
"It was a playoff type atmosphere -- and it was great to see," said Dodgers catcher A.J. Ellis, having skillfully navigated Greinke and relievers Luis Avilan and Kenley Jansen through the Giants' thrashing machine. "And it was great to see contributions all over the place."
The Dodgers used all their resources, young and old, to subdue Bumgarner and his buddies, who suddenly are in dire straits.
Falling 5 1/2 games behind the Dodgers, the Giants turn to Mike Leake with Clayton Kershaw dealing in Wednesday night's series finale.
Joc Pederson, who had been struggling at the plate, took Bumgarner deep in the seventh inning for what proved to be the winning run. Fellow rookie Jose Peraza used his athleticism to start a double play that took the Dodgers out of a troubling eighth inning after Greinke's exit.
Adrian Gonzalez -- who ended Monday night's 14-inning exercise with a walk-off single which traveled about 370 feet -- gave Greinke a lead in the third inning with a two-out single the other way, to left. It scored Peraza, who had singled with two down and moved up on Justin Turner's walk.
"When you have your ace -- one of your two aces in our case -- out there, you want to give him an early lead so he can pitch more comfortably," said Gonzalez.
Greinke breezed through six innings, giving up an infield hit to Buster Posey and nothing else. With two down after Posey's single in the second, Peraza ranged far into right center before dropping a popup off Kelby Tomlinson's bat.
Batting eighth, Bumgarner -- who has gone deep five times this season, once against Kershaw -- popped up to Peraza, who held onto this one.
The fun was just starting for Greinke. Following singles by Van Slyke and Ellis around a force out off the bat of newly acquired Justin Ruggiano, Greinke came to the plate in the bottom of the second in the No. 8 hole, with Pederson behind him.
Falling behind 0-2 in the count, Greinke worked it to 2-2 and hammered a Bumgarner slider, the bullet seemingly destined for the left-field corner. But third baseman Matt Duffy intercepted it with a backhanded stab.
"I hit it good," Greinke said, "but when I saw where he was playing, I thought he might get it. He made a nice play."
"He can flat-out hit," said Mattingly. "It was probably the most exciting part of the night for Zack. I thought it was down the line."
A relieved Bumgarner was bummed an inning later when Gonzalez stroked his first-pitch fastball in front of left fielder Alejandro De Aza for his 79th RBI of the season.
"Greinke is a great pitcher -- we know that," Gonzalez said. "We know he's going to give us his best effort every time out. He doesn't make mistakes. He can spot his fastball and then throw some nasty chase pitches. He's a great guy to play behind."
Bumgarner, coming off a dominant August, knew the importance of this assignment. The Giants are looking for some of the old magic that brought them three World Series championships since 2010.
It wasn't coming against Zack and Co.
Greinke said he "felt great" even though he experienced some pain in his right ankle pushing off a new rubber installed to replace the one sent to Cubs pitcher Jake Arrieta as a memento of his no-hitter on Sunday against the Dodgers.
The Giants threatened in the seventh with Brandon Belt's leadoff single and a walk to Posey, but Greinke pushed his way through the jam unscathed. The second out came on a called third strike on De Aza that the Giants felt was off the plate. Manager Bruce Bochy and right-hander Jake Peavy were ejected after Tomlinson flied to right for the third out.
Consecutive singles by pinch-hitter Gregor Blanco, Angel Pagan and Duffy cut the deficit in half and ended Greinke's night with one out in the eighth.
Jammed by Avilan, Belt broke his bat and was robbed when Peraza came flying over to glove the ball behind second and flip it with the leather to Jimmy Rollins for the outs that quelled the Giants' last threat. When Jansen rolled through the ninth, it was party time in Chavez Ravine.
"It was really a good game all-around," said Greinke, whose sentiment probably wasn't shared in the other clubhouse.
Lyle Spencer is a national reporter and columnist for MLB.com. Follow him on Twitter @LyleMSpencer.