SAN FRANCISCO -- San Francisco Giants manager Bruce Bochy believes his team sent a message in the first week of the season.

No, not to the three-time National League West defending champion Los Angeles Dodgers, or any of baseball's other 28 teams.

Rather, to themselves.

"We're not out of any game. That's a strong message," Bochy proclaimed after watching Joe Panik hit a two-run, tie-breaking double in the sixth inning and Johnny Cueto overcome a shaky start to deliver the Giants a third win in their four-game series with the Los Angeles Dodgers, 9-6 Sunday afternoon.

"You keep pushing," Bochy said of the mood in the Giants' dugout after they fell behind 5-0 in the first inning. "And we did."

Buster Posey, Brandon Belt and Angel Pagan hit home runs, increasing San Francisco's season-opening total to 14, as the Giants continued their home-field mastery of the Dodgers.

"Great series," Bochy insisted. "Every team that had a lead ended up losing the game in this series. The offense picked us up again."

The Giants homered in all seven of their games in the first week of the season, a franchise record for the start of a year.

Panik's hit came after Pagan had doubled and Denard Span singled to open the bottom of the sixth with the score tied at 6-6.

Panik's liner to the base of the fence in center field off Dodgers left-hander J.P. Howell scored both teammates to provide a lead that Cueto and the Giants' bullpen managed to hold until the end.

"My teammates told me to keep the game at 5-0. They would do it with the bats," Cueto said of his approach after digging a big hole in the Dodgers' five-hit first inning. "They did."

Hunter Pence's sacrifice fly later in the sixth inning scored Panik to increase the San Francisco lead to 9-6 and completed the scoring.

"Two bad outings," assessed Howell, who gave up four hits and four runs in Thursday's blown lead. "They outgrinded me. They were tougher than me."

Cueto, in his Giants home debut, settled down after the first, during which he slipped on the wet turf and had to be checked for potential ankle and back issues.

He gave up only five more hits and one more run through seven innings before turning the ball over to right-hander Sergio Romo with a three-run lead in the eighth.

Romo, left-hander Josh Osich and closer Santiago Casilla shut out the Dodgers on no hits over the final two innings, with Casilla recording his second save.

"That's what good teams are," Cueto said of the comeback. "They fall behind and they find a way to come back. I want to thank them for coming back today."

Cueto (2-0) had eight strikeouts and one walk in his seven innings. He allowed six runs on 10 hits.

Right-hander Louis Coleman (0-1), who gave up Pagan's inning-opening double in the sixth inning, took the loss.

Dodgers starter Scott Kazmir was staked to a five-run lead before taking the mound, but couldn't hold it.

Making just his second start for Los Angeles, Kazmir gave up two runs in the bottom of the first on RBI singles by Belt and Matt Duffy, then served up the homers to Posey (solo), Belt (two-run) and Pagan (solo) in the third and fourth innings while watching 5-0 and 6-5 leads to disappear.

Kazmir, who was seeking his 100th career win, left after four innings with the score tied, having allowed six runs on seven hits. He struck out four and walked one.

"I didn't have a feel for the cutter today, and a lot of my pitchers were right down the middle with no spin," Kazmir explained. "They made me pay for those mistakes."

Trayce Thompson had the big hit of the Dodgers' five-run first, a two-RBI single. Justin Turner and Austin Barnes also had run-scoring hits in the inning, and Adrian Gonzalez had a sacrifice fly.

Corey Seager singled in Chase Utley, who had doubled, in the fourth, temporarily giving the Dodgers a 6-5 lead after the homers by Posey and Belt in the bottom of the third had drawn San Francisco even.

The Giants (5-2) out-hit the Dodgers 12-10. Pagan (homer and double), Posey (homer and single), Belt (homer and single), Span (two singles) and Duffy (two singles) had two hits apiece.

Thompson had two hits for the Dodgers (4-3), who had opened the season with three consecutive shutout wins over the San Diego Padres before surrendering a total of 26 runs to the Giants.

The Dodgers have lost 11 of their last 14 games in San Francisco.

"It's always tough to lose games, especially late," Dodgers manager Dave Roberts lamented. "I mean, we could have won four games. But that's why you have to play them."

NOTES: The Giants hadn't overcome a deficit as big as five runs en route to a win since Sept. 2, 2014 against Colorado. ... The Giants' 14 home runs after seven games are their most over that span since they had 16 in the first seven games of the 2003 season. ... Dodgers LHP Scott Kazmir became the first Dodgers pitchers to yield three home runs to the Giants in a game since LHP Kazuhisa Ishii on Oct. 3, 2004. ... Dodgers SS Corey Seager extended his hitting streak to 10 games dating back to last season. ... After having run out of healthy outfielders during Saturday's 10-inning win over the Giants, the Dodgers acquired INF/OF Zach Walters and OF James Ramsey from the Cleveland Indians for cash. Both were sent to Triple-A Oklahoma City. ... In order to make room on the 40-man roster for Walters and Ramsey, the Dodgers moved OF Andre Ethier (broken leg) and RHP Josh Ravin (broken leg) from the 15-day to the 60-day disabled list. ... Both teams have Monday off before the Dodgers host their home opener Tuesday against Arizona, while the Giants begin a six-game trip in Colorado.