SAN FRANCISCO — If these San Francisco Giants were looking for motivation with six weeks left in their improbable playoff push, the 2014 team that celebrated the 10-year anniversary of its World Series title on the field before Saturday’s game provided a tried and true formula.

That group owned a middling record in August, snuck into the postseason as the final seed and rode its pitching to a third trophy in five years.

This year’s team, many of whom took in the ceremonies from the top step of the third-base dugout, faces even longer odds. But like that squad a decade prior, they seem to be hitting their stride at the right time.

Behind seven strong innings from Logan Webb and just enough timely hitting, they picked up their fourth win in a row, 3-1 over the Detroit Tigers, matching their season-long winning streak and showing increasing signs of staying power.

“We’re just grinding through games. We’re doing all the right things. Playing good defense. We finally have a full, healthy starting staff, which I think is a big deal,” Webb said. “We just have to keep it going.”

The win was the Giants’ sixth in their past seven games, their 12th in 15 since July 25, and clinched their fifth series win in a row. Improving to 61-58, the Giants moved three games above .500 for the first time all season. They pulled within 1 1/2 games of playoff position with the Mets, who hold the third wild-card spot, still yet to play.

“We’re finding ways to win games when we have to,” said third baseman Matt Chapman, who went hitless for only the third time in nine games this month but still contributed a crucial defensive play. “We wanted to start creeping over .500. It feels good. We’ve been battling all year, whether it’s injuries or just not being able to get something going, so for us to be able to start creeping in the right direction … we can’t be losing games right now because everybody seems to be winning.”

In his first official day as the Giants’ new closer, Ryan Walker was called into duty to protect a two-run lead and allowed the potential tying run to reach base with one out but painted the outside corner to ring up Dillon Dingler and snuck a slider past Javier Baez to notch his first save of the season.

Walker had one previous save last season, but he said, “this was a little more intense. Full crowd, going crazy.” He admitted he was “thinking about it a little bit” as he sat in the bullpen and once he stepped on the mound it was “nerve-wracking … but I controlled it when I was out there.”

“I’m glad he got through the first one,” Melvin said. “He definitely has the stuff and the ability to close games.”

After the Tigers touched Webb for the first run of the game in the top of the fifth, the Giants answered with three of their own in the bottom half, which proved to be enough behind their ace, who limited his opponent to one or fewer runs for his third straight start while allowing only five base runners over seven innings.

“I think I’m catching a little bit of a rhythm,” Webb said. “The changeup is probably better than it’s been all season, so try to keep riding that wave.”

Webb was in the middle of his pregame routine for the bulk of the festivities but caught Madison Bumgarner shouting him out by name and held up his water bottle.

“Those guys are what we try to be, what we strive to be,” Webb said. “I hope to be in that position some day, coming back and enjoying this. It’s what we’re all trying to do. We feed off of that. The whole clubhouse feeds off of that. … I needed to warm up, but I also wanted to listen to some of the stories that they were telling.”

Exhausting a season-high 110 pitches, Webb matched his season-high with eight strikeouts, including back-to-back punchouts to end the fifth after Parker Meadows sliced a one-out triple and scored when shortstop Tyler Fitzgerald’s throw home on a chopper from the next batter was late and offline.

The only other trouble Webb ran into came in the sixth, which he got out of with an assist from Chapman.

The Tigers were threatening with two men on and two outs, but the four-time Gold Glove-winning third baseman turned a potential run-scoring blooper into a highlight-reel catch to end the inning, leaping and twisting his body to snag Bligh Madris’ soft line drive out of midair.

“That ball gets over my head, they score and probably the other runner gets to third base,” Chapman said. “We weren’t necessarily tearing the cover off the ball today, so to be able to keep some runs off the board was huge.”

Melvin said Chapman’s catch was “such a momentum change” while Webb called him “unbelievable.”

“I don’t think many guys in baseball make that play,” Webb said. “It’s fun to pitch when he’s out there. He made the play and I was shocked, almost, like, ‘Oh, my God.’ I played with (Brandon Crawford) for a couple years and he’s one of those guys that does that sort of stuff, too. Chappy, it’s on another level.”

The No. 9 batter in the Giants’ lineup, Brett Wisely, delivered their biggest hit of the day, poking a double past the bag at first base that drove home Mike Yastrzemski and Jerar Encarnacion, who led off the inning with back-to-back base hits.

Wisely’s RBI knock gave the Giants their first lead, 2-1, and Heliot Ramos singled him home to make it 3-1.

Once again, all of the Giants’ scoring came in the fifth inning or later.

“I think there’s a real confidence late in games that we’re going to do our best work, and it’s showed up so many times this year,” Melvin said. “We talk about it a lot. We talk about how we’re able to score off the best pitchers — closers, set-up guys — late in games. It shouldn’t take away from an urgency in the beginning of the game, but that keeps showing up where our best at-bats come in big situations later in the game.”

Up next

The Giants will go for a season-high fifth win in a row while looking to clinch only their third series sweep of the season Sunday with RHP Hayden Birdsong (3-1, 4.73) scheduled to face RHP Keider Montero (2-5, 5.62). First pitch is scheduled for 3:05 p.m. ET.

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