SAN FRANCISCO -- The Giants outlasted the Dodgers in a division race for the ages. But they couldn’t hold off their archrivals when it mattered most.

Cody Bellinger delivered a go-ahead single off rookie reliever Camilo Doval in the ninth inning to lift the Dodgers to a 2-1 win in the decisive Game 5 of the National League Division Series on Thursday night at Oracle Park, ending the Giants’ historic season in the most heartbreaking of fashions.

Max Scherzer, pitching on two days’ rest after starting Game 3, took the mound in the bottom of the ninth and struck out Wilmer Flores on a controversial check-swing call to leave the tying run at first base and seal the win for the Dodgers, who will now advance to the NL Championship Series to face the Braves.

Flores appeared to check his swing on an 0-2 slider, but first-base umpire Gabe Morales ruled that he went around on appeal, abruptly ending one of the most compelling chapters of the storied Giants-Dodgers rivalry.

“Super tough,” Giants manager Gabe Kapler said. “Obviously, you don't want a game to end that way. I know these guys work really hard to make the right call, so it's super challenging on our end. ... There are other reasons we didn't win today's baseball game. That was just the last call of the game.”

It was a bitter ending for the Giants, who stunned the baseball world by winning a franchise-record 107 games to edge the 106-win Dodgers for the coveted NL West title on the final day of the regular season.

It felt inevitable, predestined even, that the two behemoths would meet again in the postseason, and their highly anticipated October clash didn’t disappoint, with the Giants and Dodgers splitting the first four games of the NLDS to set up a winner-take-all Game 5.

Given how evenly matched the clubs were all year, it was only fitting that their 24th and final showdown of the year was tied, 1-1, heading into the ninth.

Doval, who entered Thursday riding a 19 1/3-inning scoreless streak over his previous 18 appearances, needed only one pitch to record the final out of the eighth, but he fell into trouble in the top of ninth, when he hit Justin Turner and gave up a single to Gavin Lux that put a pair of runners on for the Dodgers with one out. That brought up Bellinger, who exorcised a miserable season by shooting a 1-2 slider to right field for a shift-busting single that drove in Turner and put the Dodgers ahead.

Budding ace Logan Webb said the first thing he did when he returned to the clubhouse after the game was hug Doval, who emerged as the Giants’ most electric reliever over the final month of the season.

• Doval has 'bright future' despite G5 setback

“He feels awful, which is kind of brutal because he pitched so [well] for us,” Webb said. “He did so well. For him to be the guy who gave up the run, it just sucks. But he's going to be a big part of this team for a long time.”

The same can be said for Webb, who backed up his brilliant start in Game 1 with yet another gem against the Dodgers on Thursday, working seven innings of one-run ball to end his first career postseason with a 0.61 ERA over 14 2/3 innings.

“His last three starts were as pressure-packed as could be, and he answered the bell every time,” Buster Posey said. “I’m excited for him. I’m really excited for the Giants organization, to have a young pitcher like that to build around.”

Webb allowed only four hits, three of which came off the bat of Mookie Betts, who singled, stole second and scored on Corey Seager’s RBI double to give the Dodgers a 1-0 lead in the sixth inning.

Still, the Giants quickly answered back on Darin Ruf’s towering solo shot to start the bottom of the sixth. Ruf, who produced long flyouts of 377 and 378 feet in his first two at-bats of the night, crushed a misplaced fastball from Dodgers lefty Julio Urías 452 feet to straightaway center field, tying the game at 1.

It was the first career postseason hit for the 35-year-old Ruf, who broke into the Majors with the Phillies in 2012 and spent three years playing in Korea before joining the Giants on a Minor League deal ahead of the 2020 season. He went hitless in his first nine at-bats against the Dodgers before coming through with the longest home run of the postseason.

In the end, the rest of the Giants’ offense, which led the NL in home runs and ranked second in runs, couldn’t do enough against the Dodgers’ deep stable of arms, which included an opener in Corey Knebel, which helped neutralize the Giants’ platoon advantage against Urías on Thursday. San Francisco scored only 10 runs over five games and didn’t come through with enough big hits to topple Los Angeles, hitting only .182 with a .513 OPS in the postseason.

“I think everybody in that locker room can hold their head high,” Posey said. “From day one, it was giving everything you had in your preparation and all the way to the finish. I know I’ve been a part of a run like this to where it seemed like the last month of the season was playoff games. We played a tight game to finish here; obviously, we would have rather come out on the other side, but I’m happy it ended up being a tight game and coming down to the wire.”

Still, the Giants will head into the offseason with a bright future and plenty of key decisions ahead, most notably making a call on Posey’s $22 million club option for 2022, which is likely to be picked up following the 34-year-old’s resurgent campaign this year.

Posey, for his part, remained noncommittal about his future, saying, “I’m definitely just going to take some time with my wife and talk with her. Be able to be a full-time dad to four kids for the first time in a while. Just kind of take it slow and see how things progress.”

With their mix of revitalized veterans like Posey and Brandon Crawford and emerging young arms like Webb and Doval, the Giants certainly appear to have the pieces to turn themselves into a sustainable contender, which could set the stage for plenty of future postseason matchups with the Dodgers.

“This won't be the last time we play them in the playoffs,” Webb said.