SAN FRANCISCO Madison Bumgarner insists he has no idea why he was virtually unhittable in August.

But the San Francisco Giants ace does know this: He loves playing with Marlon Byrd.

Staked to an early lead thanks in large part to a three-run homer by Byrd, Bumgarner struck out 12 batters in just six innings for the first time in his career Thursday afternoon, pitching the Giants to a 9-1 victory over the Chicago Cubs and a 2-1 series win in a battle of National League playoff contenders.

"He's 2-for-2 with three-run homers on my days," Bumgarner said of Byrd, who was acquired Aug. 20 from the Cincinnati Reds. "I'll take 'em."

Byrd's three-run shot came in the third inning, and second baseman Kelby Tomlinson hit his first major-league homer -- an eighth-inning grand slam -- as the Giants exacted a small measure of revenge after getting swept by the Cubs in a four-game series in Chicago earlier this month.

Afterward, it was clear which home run excited Byrd the most.

"He was trying to hold it in," the veteran said of the rookie's grand slam. "I don't like holding it in. I told him, 'You're young. Enjoy it.'"

The Giants' win, the 15th in their last 18 home games, allowed them to match the Los Angeles Dodgers' victory earlier in the day at Cincinnati. San Francisco (68-59) remains 2 1/2 games behind the NL West leaders.

The Cubs, meanwhile, dropped their second in a row on the eve of heading to Los Angeles to face Dodgers ace Clayton Kershaw in the opener of a three-game series Friday night. Chicago (73-53) fell 3 1/2 games behind idle Pittsburgh (76-49) in the battle for the NL's first wild-card spot.

Chicago responded to the second straight loss with a trade, acquiring right-handed reliever Fernando Rodney from the Seattle Mariners for a player to be named and cash.

"You've got to learn how to understand and bounce back from a loss," Cubs manager Joe Maddon said. "The way you do that: You're maybe upset for about 30 minutes and you move on."

Bumgarner ran his August record to 5-0 with six innings of two-hit ball.

Both hits came in succession in the second inning, when Cubs first baseman Anthony Rizzo singled and scored on a double by second baseman Starlin Castro.

Other than one walk later in the inning and another in the fifth, the Cubs had no other baserunners against the reigning World Series Most Valuable Player, who left after throwing 98 pitches.

"We had a chance to give him a break," Giants manager Bruce Bochy said when asked why he pulled Bumgarner relatively early. "We've been riding him pretty hard this month."

The double-digit strikeout effort was his third of the month, with the others -- 12 against Houston on Aug. 11 and a season-best 14 against Washington on Aug. 16 -- coming in complete games.

He had never struck out more than 11 batters in a start lasting six innings or less.

Bumgarner (16-6), who is not scheduled to pitch again this month, will finish August with 53 strikeouts and just five runs allowed in 37 2/3 innings (1.19 ERA).

"Man, I don't know. I'm just going out there and competing," he said of his August flurry, which rivaled his October run last season. "Right now, my body feels good. Command feels good. That's the main thing: Delivery feels right. Then everything falls into place."

Byrd produced a majority of the Giants' early scoring with his home run in a four-run third. It was his 21st of the season.

After the Giants had countered the Cubs' run with an RBI double by center fielder Juan Perez in the bottom of the second, third baseman Matt Duffy put San Francisco on top in the third with a single that scored left fielder Nori Aoki.

One out later, Byrd smacked his second homer in six games as a Giant, a three-run shot to straightaway center field that gave Bumgarner a 5-1 cushion.

"It was good to see the offense break out like that," Bochy said. "Getting a cushion like that is what made the move (to pull Bumgarner early) possible."

Aoki nearly added to the Giants' total in the sixth when he sliced a liner past diving left fielder Chris Denorfia. But Denorfia recovered in time to get the ball to shortstop Addison Russell, whose strong relay throw to the plate beat Aoki by a matter of inches.

Cubs starter Dan Haren (8-9) was pulled one out into the seventh, having allowed five runs and six hits in 6 1/3 innings. He walked three and struck out four.

"I settled in a little bit as the game went," the veteran said. "I didn't tax the bullpen like I had before, so at least that's good. But I've got to be better."

Tomlinson's grand slam capped the Giants' scoring in the eighth against the third Cubs pitcher, left-hander James Russell. It followed a double by catcher Buster Posey and two walks, including one intentional to Byrd, bringing the rookie to the plate.

Tomlinson, Posey and Perez had two hits apiece for the Giants, who outhit the Cubs 10-3.

NOTES: The Cubs demoted LHP Zac Rosscup, who pitched two-thirds of an inning on Thursday, to Triple-A Iowa to create a roster spot for RHP Fernando Rodney. ... The last Giants rookie to hit a grand slam was SS Brandon Crawford in 2011. ... Giants LHP Madison Bumgarner has struck out 10 or more batters 25 times in his career. ... Facing Bumgarner, the reigning World Series Most Valuable Player, added to the Cubs' award-winning week. They'd already gone up against two Cy Young Award winners -- Cleveland Indians RHP Corey Kluber on Monday and Giants RHP Jake Peavy on Wednesday. ... The Cubs are scheduled to face the Los Angeles Dodgers' Cy Young Award-winning Clayton Kershaw in the opener of a three-game series Friday night. ... The Cubs are hoping to have CF Dexter Fowler (sore hand, shin) back in the starting lineup Friday. X-rays on Fowler's shin, injured on a foul ball Tuesday, were negative, but he was held out of the starting lineup for a second consecutive day. ... Cubs rookie Kris Bryant made his first start in right field.