SAN FRANCISCO -- There are more than regional bragging rights at stake in this year's Bay Bridge Series between the Giants and A's. Both clubs are in the Wild Card mix in their respective leagues, adding an extra degree of importance to these Interleague games.

The Giants were able to further their cause at their cross-bay rivals' expense Tuesday, riding a brilliant effort from Madison Bumgarner to a thrilling 3-2 series-opening win over the A's at Oracle Park.

“That was a good all around ballgame for us,” Bumgarner said. “Every little thing we did paid off in the end. We won a close game there.”

• Box score

Bumgarner allowed only a home run to Stephen Piscotty over seven innings, outdueling A’s counterpart Brett Anderson, who carried a shutout into the sixth inning before the Giants’ offense finally began to stir.

Buster Posey, Evan Longoria and Kevin Pillar delivered three consecutive two-out doubles to erase a one-run deficit and put the Giants ahead, 2-1, in the sixth. Bumgarner hit for himself in the seventh and laid down a bunt that helped set up a key sacrifice fly from pinch-hitter Scooter Gennett.

The A's made it interesting in the ninth, loading the bases with one out against closer Will Smith. Matt Chapman came within inches of tying the game after sending a deep fly ball to the left-field corner, but Smith caught a break after it curled foul.

“Go foul, please,” Smith said when asked what went through his head at that moment. “I was walking down the line just to see if hopefully it’d go foul. Thank God it did.”

Mark Canha worked a walk to force in a run and bring Oakland within one, but Smith struck out Chad Pinder on his 37th pitch of the night to seal the Giants’ win and pick up his 29th save of the season.

“We had to put some torture in there at the end,” manager Bruce Bochy said. “Smitty showed a lot about what he’s about. His pitches were up there, and the last pitch he let go pretty good and got it by him. Great ballgame. Well-pitched game, timely hitting. They came back, but we found a way to get the last out.”

After opening their homestand with a sweep at the hands of the Nationals, the Giants (60-60) have now won three in a row to climb back to .500 and pull within 3 1/2 games of the National League Wild Card race.

Bumgarner extended his recent stretch of dominance against the A’s, yielding only two hits while striking out nine and walking none. The 30-year-old left-hander has logged a 2.61 ERA over his last 10 outings, with the Giants winning nine of those starts. Bumgarner’s 17 quality starts are tied for the second-most in the NL, behind only Dodgers lefty Hyun-Jin Ryu (19).

The lone blemish for Bumgarner came in the fifth, when he surrendered Piscotty’s shot on an inside fastball. Marcus Semien delivered the only other hit off Bumgarner, leading off the game with a popup to shallow right field that first baseman Aramis Garcia, a catcher by trade, allowed to fall for a single.

“He was just commanding all his pitches and attacking the zone for a lot of strikes,” Piscotty said. “We did our best. He’s a great pitcher. You just have to tip your cap and go get them tomorrow.”

Bumgarner has become a vital anchor for the Giants’ pitching staff, which is down to three starters following the injury to Shaun Anderson and Conner Menez’s demotion to Triple-A Sacramento. The Giants have received inconsistent performances from the back end of their rotation, which has featured a trio of rookies in Anderson, Menez and Tyler Beede, but Bumgarner and fellow veteran Jeff Samardzija have combined to form a reliable tandem at the front end.

“He’s our guy,” Bochy said. “Your No. 1, they’re invaluable. You’ve got to have a guy like that, I think, if you’re going to have success.”