SAN FRANCISCO -- On a day when former teammate Aroldis Chapman was traded, Cincinnati Reds slugger Jay Bruce went out and increased his own value Monday night.

Bruce smacked a pair of two-run home runs, and the Cincinnati bullpen added to an impressive month of July with four shutout innings to rescue unbeaten Anthony DeSclafani, leading the Reds to a 7-5 victory over the San Francisco Giants in the opener of a three-game series.

Eugenio Suarez followed Bruce's first homer with a two-run shot of his own, helping the Reds run their record since the All-Star break to 7-3.

"We won today," said DeSclafani (6-0), the majors' only unbeaten pitcher with a minimum of seven starts. "That's all that matters."

It might also matter that Bruce, whose name has come up in trade rumors on almost a daily basis, improved his stock with the 20th two-homer game of his career in a ballpark known to be pitcher-friendly.

He never previously had a two-homer game in San Francisco, where he managed just two home runs in his first 82 at-bats before the personal back-to-back in the fourth and sixth innings.

"Usually if I hit it," he said, "it doesn't matter what field I'm in."

The homers by Bruce and Suarez in the fourth inning gave the Reds a 4-1 lead.

After two-run shots by the Giants' Brandon Belt and Angel Pagan pushed San Francisco back into the lead at 5-4 in the fifth, Bruce duplicated his feat in the sixth to give the Reds a lead they never relinquished.

The power display came just hours after the Chapman trade provided Bruce a dose of reality.

"Seeing trades is always interesting," he said. "A lot of people have gone through it before, and I'm not going to be the last."

The loss was San Francisco's eighth in nine games since the break, and it ended a four-game home winning streak.

"These ruts are tough things you get into," Giants manager Bruce Bochy said. "The long ball is hurting us right now. There's no getting around that. They have a lot of power in that club. If you make a mistake, there's a chance you'll pay for it."

DeSclafani benefitted from both the home runs and the bullpen effort after allowing five runs and six hits in five innings. He walked two and struck out six.

After Bruce's second two-run shot in the sixth, the Cincinnati bullpen dominated the game, with right-handers Jumbo Diaz and Raisel Iglesias and lefty closer Tony Cingrani combining to retire 12 of the 13 batters they faced. Cingrani recorded his 11th save with a one-hit ninth.

Reds relievers have a combined 2.42 ERA in July after they were torched to the tune of 6.21 in April, 7.25 in May and 4.77 in April.

"We talk about it a lot ... the pitching staff we envision," Reds manager Bryan Price said. "We're getting closer."

The Reds gave Cingrani a two-run cushion when Billy Hamilton squeezed home Suarez, who had doubled, in the top of the ninth.

Jake Peavy (5-9) took his first loss when facing an opponent for the second time in the same season as a member of the Giants. He had been 9-0 and the Giants 12-0 under those circumstances before Monday.

The veteran gave up all three Reds homers and six runs in five-plus innings. He allowed only four hits, walked two and struck out five.

"I'm disappointed in my effort after we came back and got the lead," said Peavy, who has given up seven of his 15 home runs this season in two starts against the Reds. "For some reason, I don't know why, I went away from what was successful there in those first few innings. It got me."

The two homers gave Bruce four in his past three games. He is tied for the National League lead with 77 RBIs.

Bruce, Suarez and Joey Votto scored two runs apiece for the Reds, who were coming off a nine-game homestand during which they recorded 2-1 series wins over the Milwaukee Brewers, Atlanta Braves and Arizona Diamondbacks.

Belt, who was moved down in the lineup from third to sixth after a 2-for-33 stretch, had three of the Giants' seven hits.

Denard Span had two hits and scored twice for the Giants, who were opening a seven-game homestand.

NOTES: Only two players in Reds history -- RF Frank Robinson (32) and 1B Adam Dunn (22) -- have more multi-homer games than RF Jay Bruce (20). ... Reds 1B Joey Votto extended two streaks in the game -- his hitting streak to 10 straight with a sixth-inning double and his run of consecutive games with at least one walk to eight with a free pass in the fourth. ... The Reds announced before the game that RHP Homer Bailey (elbow surgery) will join the club in San Francisco on Tuesday after having made his sixth rehab start at Triple-A Louisville on Monday night. Bailey threw 98 pitches, allowing two runs in 4 1/3 innings. ... Giants 1B Brandon Belt has gone 23-for-40 (.575) in his past 10 games against the Reds. ... Giants 2B Joe Panik (concussion) is scheduled to begin a rehab stint at Triple-A Sacramento on Tuesday.