OAKLAND — Giants manager Bob Melvin wanted to take time to appreciate his final game at the Coliseum, so he made sure to beat the rush by arriving at 7:15 a.m. on Sunday morning.

Just as he did during his 11 seasons at the helm of the A’s, Melvin ran the stairs and looked up at the retired numbers of the Oakland greats that crown the top of Mount Davis. He caught up with security guards, ballpark vendors and other staffers. He wore white shoes — a nod to the A’s signature look — and took out the lineup card, allowing him to soak in every moment of the final Bay Bridge Series game.

“It’s sad, first of all, because it’s going to be the last game that I’ll be here,” Melvin said. “There’s a lot to it today. There’s a lot of emotions to it today. … I’ve spent a lot of my life here.”

The Giants made sure Melvin’s final memory of the Coliseum would be a good one, as Jerar Encarnacion and Michael Conforto launched back-to-back home runs in the top of the 10th inning to lift the club to a dramatic 4-2 win over the A’s in Sunday afternoon’s series finale.

“It was kind of [appropriate] that the game ended like that,” Melvin said. “When I was here, we had so many walk-offs and so many extra-inning wins and so many close games. The fans are going crazy. Both sides going crazy. I don’t know how it could have been more perfect to end it like this — obviously, with us winning.”

The late homers ensured the Giants didn’t squander another dominant start from left-hander Blake Snell, who struck out 10 over seven innings of one-run ball. Snell now has a 1.03 ERA over his last eight starts and has reached double-digit strikeouts in four of his last five outings. The two-time Cy Young winner has racked up 55 strikeouts over his last five starts, passing John Montefusco (54 in 1975) for the most in a five-game span by a Giants pitcher since at last 1901.

“He looks untouchable,” Conforto said. “We know he’s going to give us a chance. We know he’s going to give us everything he’s got.”

The A’s opened the scoring on Miguel Andujar’s RBI single in the sixth and then had Snell on the ropes in the seventh after loading the bases with one out. But Snell struck out Max Schuemann swinging on a curveball and then battled back from a 3-0 count to coax an inning-ending groundout from Daz Cameron on his 109th and final pitch of the afternoon.

“When I got 3-0 against Daz, I was like, ‘If I’m losing, that’s because you’re getting a fastball,’” Snell said. “That was kind of my approach, my mentality. I was going to throw the best three fastballs I got and see what he can do.”

The Giants’ slumping offense — which was shut out on Saturday and entered Sunday slashing only .199/.268/.303 since Aug. 9 — struggled to provide Snell with much run support, as they were blanked through the first six innings by A’s lefty JP Sears. Their recent stretch of futility led to some overaggressiveness on the bases, as Encarnacion was thrown out trying to stretch a single into the double in the second and Mike Yastrzemski and Tyler Fitzgerald were both caught stealing by Oakland catcher Shea Langeliers.

San Francisco finally scored its first run of the series in the seventh, when Heliot Ramos led off with a mammoth 448-foot shot that banged off the top of the hitter’s backdrop in center field. It was the longest home run of Ramos’ career and the second-longest by a Giant at the Coliseum since Statcast began tracking in 2015, behind only Jarrett Parker’s 454-foot blast on Sept. 25, 2015.

“It didn’t feel like anything we were going to do was potentially going to score a run, and all of a sudden it’s a homer and it’s a completely different feeling,” Melvin said.

The Giants went ahead for good in extra innings, with Encarnacion drilling a first-pitch fastball from Dany Jiménez over the center-field wall to score automatic runner Matt Chapman and snap the 1-1 tie. Conforto then came off the bench and smoked a hanging slider out to right field, extending San Francisco’s lead to 4-1.

The insurance run provided extra breathing room for closer Ryan Walker, who went out for a second inning after the Giants took the lead in the top of the 10th. The A’s pulled within two after automatic runner Lawrence Butler scored on an error by second baseman Brett Wisely and went on to load the bases with no outs, but Walker struck out the next three batters he faced to escape the jam and close out the win for San Francisco.

Two former A’s — Chapman and Mark Canha — walked away from their final game at the Coliseum with some keepsakes. Chapman requested and received the third-base bag, while Canha scooped up some infield dirt to take home. Melvin, for his part, didn’t feel the need to seek out any souvenirs.

“I think just being here today is enough,” Melvin said.