OAKLAND, Calif. -- Shortly after the Boston Red Sox arrived at their team hotel in San Francisco on Sunday night, third baseman Pablo Sandoval received his 2015 World Series ring in a ceremony with Giants manager Bruce Bochy, president Larry Baer and general manager Bobby Evans.

Sandoval's Bay Area homecoming celebration continued Monday night when he led off the top of the 11th inning with a tiebreaking home run off reliever Angel Castro, lifting the Red Sox to a 5-4 victory against the Oakland at the O.co Coliseum.

"It was exciting and emotional," said Sandoval, who won three World Series as a Giant before signing during the offseason with Boston as a free agent. "You get the ring, then hitting a homer to win the game. It was a big day for me."

After falling behind 0-2 in the count, Sandoval crushed a high and inside 94 mph fastball from Castro (0-1), who made his second career major league appearance. The home run was Sandoval's fourth of the season and second in two games.

"Hopefully, this was a little bit of a homecoming for him," Red Sox manager John Farrell said. "Not only to the area, but for what he's had with the Giants and the ability to meet with so many people last night when we got in. Today was a special day for him."

Right-hander Matt Barnes (1-0), Boston's sixth reliever of the game, earned his first major league win, blanking the A's in the 10th and 11th innings on no hits.

"He was calm, pulse seemed to stay pretty even-keeled for him," Farrell said. "Didn't go out and change his demeanor after we took the lead in the 11th inning. Two key innings for us."

Rookie catcher Blake Swihart went 2-for-5 with a double and scored two runs for the Red Sox, who won back-to-back games for the first time since April 20-21. Center fielder Mookie Betts went 2-for-5 with two RBIs.

The A's (12-22) lost their season-high sixth straight game and fell to 0-6 in extra inning games and 1-11 in one-run games.

"You really have to persevere to keep your fight the way things have been going in these type of games for us," A's manager Bob Melvin said. "Just going to have to work a little harder. It's the same story here. It's getting tough to explain. It seems like we've played this game so many times this year that it's a little bit surreal. But we have to come out tomorrow and try to break through."

Oakland designated hitter Billy Butler went 3-for-5 with a double, a run and an RBI. Right fielder Josh Reddick went 2-for-4 with two walks and a run. Catcher Stephen Vogt had a double and two RBIs in four at-bats.

Red Sox right-hander Rick Porcello gave up three runs on nine hits over five innings and didn't figure in the decision.

A's left-hander Scott Kazmir allowed just two runs on four hits over six innings but got a no-decision.

"We just need to be positive," Kazmir said. "It can be to where we just make it bigger than what it is. I don't think we're concerned about it. We have a lot of young guys that can't be rattled."

The A's led 3-2 through six innings, but that was it for Kazmir, and the Red Sox scored twice in the seventh off right-handed reliever Evan Scribner. Shortstop Xander Bogaerts blooped a one-out single to right, moved to third on Swihart's single and scored on a single by Betts, with Swihart moving to third.

Second baseman Dustin Pedroia hit a comebacker to Scribner, who threw to second for what looked to be the start of a double play, but shortstop Marcus Semien couldn't get the ball out of his glove and was upended by a sliding Betts as Swihart scored.

Oakland answered with a run in the bottom of the seventh off left-hander Craig Breslow. Reddick lined a leadoff single, went to third on Butler's single to center and scored on Vogt's sacrifice fly.

Four innings later, Sandoval made Castro pay, lining his 0-2 pitch over the fence.

"I don't know that there's much an opposing pitcher's going to set up," Farrell said. "He's not looking to take pitches. Plate coverage, he covers it from head to toe. Even tonight, an 0-2 fastball that's up over the plate, he squares the ball up. He can square up so many different types of pitches and locations. Sure it helps him, and he hits really good stuff, good velocity, good action pitches. No bigger than tonight."

NOTES: RHP Edward Mujica was added to Oakland's 25-man roster Monday, two days after the reliever was acquired from Boston for cash or a player to be named, and he threw a scoreless inning. A's RHP Chris Bassitt was optioned to Triple-A Nashville, opening a roster spot for Mujica. ... Red Sox RF Shane Victorino (right hamstring tightness) was activated from the disabled list and went 0-for-4. He played two rehab games for Double-A Portland. ... Red Sox INF Luis Jimenez was designated for assignment, opening a roster spot for Victorino. Jimenez was claimed off waivers from Milwaukee on May 3 and went hitless in one at-bat with Boston. If he clears waivers, the Red Sox want him to remain in their organization, manager John Farrell said. ... A's LHP Sean Doolittle (strained left shoulder) threw 23 pitches in his second simulated game. Doolittle will pitch next in an actual game, either at extended spring training or for one of the Athletics' minor league affiliates.