SAN FRANCISCO -- One down, three to go for the San Francisco Giants.

Even that might not be good enough to catch the Los Angeles Dodgers in the National League West this week, but the defending champs aren't going down without a fight.

Pinch-hitter Alejandro De Aza's sacrifice fly scored Marlon Byrd from third base in the bottom of the 12th inning Monday night as the Giants kept their slim playoff hopes alive by beating the Dodgers 3-2 in the opener of a four-game series between the top two teams in the West.

Right-hander Jake Peavy pitched seven strong innings and catcher Trevor Brown had a two-run double as the Giants (82-74) kept the Dodgers (87-69) from clinching the NL West, trimming their lead to five games with six remaining.

"As a professional athlete, you love to be in a position like tonight," Peavy said. "It was like a Game 7. You have to win."

The Dodgers, who lost four in a row, can clinch their sixth division title in the past 10 years Tuesday when ace left-hander Clayton Kershaw opposes reigning World Series Most Valuable Player Madison Bumgarner of the Giants.

The two teams also are scheduled to meet Wednesday and Thursday.

Any Dodgers win in the series would wrap up the West and slot L.A. against the New York Mets in the first round of the NL playoffs.

"We had 'em. It was right there at our fingertips," Dodgers right fielder Andre Ethier said. "One little bounce ... you get a little hop here and we walk away with a win."

After the Dodgers had come from behind to forge a 2-2 tie against the San Francisco bullpen in the top of the ninth inning, the Giants rallied for the must-win in the last of the 12th after Byrd greeted right-hander Yimi Garcia (3-5), the seventh L.A. pitcher, with a single.

Second baseman Kelby Tomlinson followed with his second hit of the game, a single to right field, sending Byrd to third.

After Brown grounded to third against a five-man infield for the inning's first out, De Aza hit a fly ball plenty deep into left field off Dodgers left-hander Adam Liberatore to give the Giants their third straight win.

"It's all about going hard, they say, for nine innings," Giants manager Bruce Bochy said. "Tonight it went a little longer than that."

The Dodgers stranded the potential go-ahead run in scoring position in three of the last four innings.

Right-hander Hunter Strickland (3-3), the sixth Giants pitcher, got the win after pitching 1 2/3 innings of one-hit relief.

The Giants took a 2-1 lead into the top of the ninth, but the Dodgers rallied to tie after shortstop Corey Seager and first baseman Adrian Gonzalez led off with singles off left-hander Josh Osich.

After Giants closer Santiago Casilla entered the game and a sacrifice bunt advanced the runners to second and third, Ethier produced a 2-2 tie with a grounder to second base, scoring Seager.

Casilla escaped further damage by getting Dodgers second baseman Chase Utley to ground to shortstop, stranding pinch-runner Ronald Torreyes at third.

The blown save was Casilla's sixth of the season.

In helping the Giants run their home record to 7-0 against the Dodgers this season, Peavy limited L.A. to three hits and one run in seven innings. He walked one and struck out four.

"Five-game lead with six to play. I don't think you can call that pressure," Peavy said of the Dodgers' situation. "That said, we have control over these next three (games)."

Like Peavy, Dodgers starter Zack Greinke had nothing to show for seven innings of quality work. He allowed two runs on four hits, walked three and struck out seven.

"Really intense game," Greinke noted. "I thought we played great, and they played real good, also. Peavy pitched as good as I've seen him pitch."

Greinke was pitching for the first time in 10 days, having missed a start due to a calf injury.

One of the hits Greinke allowed was Brown's two-out, two-run double in the second inning that provided all the Giants' scoring until the 12th. Brown had totaled just three RBIs in his first 22 at-bats for the Giants.

He and Tomlinson had two hits apiece for San Francisco.

"The boys were fighting," Bochy said. "I'm glad they got a win the way they were playing tonight."

Seager, Ethier and late-game replacement Enrique Hernandez each had a pair of hits for the Dodgers, who used 25 players in the game.

"I was happy with the way our guys played," Dodgers manager Don Mattingly said. "It seemed as the game went on, our guys' focus got better and better."

Both teams finished with nine hits.

NOTES: The Giants clinched a winning record with their 82nd win of the season. ... The walk-off win was the Giants' sixth of the season. ... OF Alejandro De Aza's walk-off RBI was the fourth of his career. ... SS Corey Seager's RBI single in the third inning ended the Dodgers' 36-inning scoring drought against the Giants. ... The Dodgers' franchise record for consecutive losses in San Francisco is nine, a streak that bridged the 1961 and '62 seasons. ... The Dodgers reinstated INF/OF Enrique Hernandez (strained left hamstring) from the disabled list Monday. ... As a reminder to the Dodgers of their recent success, the Giants displayed their 2010, '12 and '14 World Series championship trophies behind the plate before the game.