Jul. 7—SAN FRANCISCO — With a onerun lead to secure and without their All-Star closer to do it, the Cardinals turned to a reliever who, less than 100 hours ago, had been on waivers and as uncertain about where his season was headed individually as the Cardinals were collectively.

Justin Miller got the final two outs of a gripping win.

Credit rookie Dylan Carlson with the save.

With two on and two out, San Francisco’s Jason Vosler lofted a fly ball into a wind that gusted so strong at Oracle Park that Adam Wainwright felt himself leaning on the mound, that a cameraman couldn’t steady his shot as he broadcast a singer from the field. Carlson eased back to the warning track, to the wall, and leaped to snag Vosler’s carrying fly ball to keep it from bringing home the winning run. The catch cinched a 6-5 victory against the Giants on Tuesday and assured the Cardinals’ a series victory against the team with the best record in the National League.

The consecutive wins this week against the Giants are the first two-game winning streak for the Cardinals this season against an opponent with a winning record at the time.

“It’s just validation that we should be playing a lot better than we have been,” Wainwright said. “We’re a better team than we’ve show. The couple of games we beat a tough team, in their park, with a tough crowd to play in front of. Tough place to win. And we won two really tough games.”

The Cardinals played from ahead for the entire game. They got a two-run homer from Nolan Arenado to start their scoring, a two-run single from Paul Goldschmidt to break a tie, and an all-around performance from rookie Edmundo Sosa. The Cardinals gained the lead, added to it, and then went about finding someone to cement it. Closer Alex Reyes and Giovanny Gallegos were hands-off based on recent usage, and the matchups in the ninth made it possible to utilize Miller. The righthander was plucked off waivers and added to the team Saturday and within four games found himself closing out a pivotal win, the one that gave the Cardinals the series.

Miller retired both batters he faced and stranded the two runners he inherited.

“Shoot, everybody put their piece into that game,” manager Mike Shildt said. As much scrutiny as the Cardinals have brought on their lineup and the dissection of its every unsteady aspect, this quest for more consistent run-scoring comes down to simplest of math. An offense’s lead is only as good as the pitchers who keep it. The more the Cardinals stayed ahead of the Giants with a drumbeat of runs, the more latitude they had to cover the late innings without using two of the best pitchers. Arenado’s homer in the first inning gave them the 2-0 lead, and they did not stop. They added on — and on. And often against a familiar face.

John Brebbia, signed by the Giants after the Cardinals let him become a free agent this winter, made his sixth appearance since returning from elbow surgery and his first against his former team. One of the Cardinals’ most reliable middlemen in relief during Shildt’s first seasons as manager, Brebbia retired the first former teammates he faced. Then he ran into the Cardinal he never called a teammate — and one who knew him best of all.

Arenado’s third hit of the game was a single to right off Brebbia. The Cardinals’ third baseman, acquired a few months after Brebbia became a free agent, then stole second when he had Brebbia’s timing.

That put him in scoring position for Yadier Molina.

The catcher who shepherded Brebbia through so many of his 161 appearances for the Cardinals got a pitch that was above his chest, higher than the zone, and still pulled it to left for single that scored Arenado because of the steal. Rookie Sosa hit a solo homer off Brebbia with two outs in the eighth inning to give the Cardinals a three-run lead his diving play in the eighth would help defend.

The Giants, analytically driven and deep, have aggressively used their bench for better matchups. Manager Gabe Kapler sent three consecutive pinch hitters to the plate Monday in the eighth inning, and when lefty Andrew Miller entered in the sixth out came Darin Ruf, a righthanded batter, in place of the left-handed-hitting starter at leadoff. The matchups seesawed from there, and righthander Ryan Helsley faced Ruf in the eighth. The Giants’ outfielder squeaked a grounder that seemed bound for right field when Sosa dashed over from his shifted spot, dove for the ball, and completed the throw for the second out of an inning going sideways. “Huge play,” Shildt said.

Genesis Cabrera inherited a runner on base, allowed two hits, saw the tying run record second base, and then struck out pinch-hitter Thairo Estrada to preserve a one-run lead.

The last pitch Wainwright threw made for a good defensive play in right field that saved at least a run, probably two. The last pitch Cueto threw became a play he had to make.

With a streak of six consecutive quality starts coming into Tuesday’s game, Wainwright did not have the expedient innings to get deeper into the game before nosing up against 100 pitches. The righthander dealt with a runner on base every inning, and in four of his five innings had at least two. The three runs he allowed all came as RBIs for Giants All-Star shortstop Brandon Crawford. The Gold Glove-winner singled to bring home two runs with a two-out single in the third, and when his turn came around in the fifth he doubled to narrow the Cardinals’ lead to a run.

Without a good feel for his fastball and aware the Giants knew that as they keyed on his breaking pitches, Wainwright had pitched a scoreless fourth immediately after the Cardinals retook the lead, and he slipped through the fifth thanks to a diving catch in right.

The Cardinals opted to intentionally walk Steven Duggar, a lefthanded batter, to get the matchup with No. 8 hitter, catcher Chadwick Tromp. That put the go-ahead run on base with Crawford already in scoring position. The Cardinals expected to go back to their ideal outfield configuration with Tyler O’Neill in left and at cleanup, but he had a severe allergic reaction to what he ate a few hours before the game and had to be taken to a hospital. That put Tommy Edman back in right — and he had just enough length to dive forward and steal a single from Tromp on Wainwright’s 97th pitch.

“My stuff was terrible,” Wainwright said. “Really bad. Horrible fastball command. I cannot remember the last time I bounced two fastballs. Bad fastball. Bad fastball command, bad at-bat command, bad fastball life which we knew pretty on. Yadi had a lot of the crooked fingers going tonight, a lot of twos and three and so got a little predictable on my part.”

In the top of the next inning, Jose Rondon pinch-hit for Wainwright and came a Johnny Cueto juggle shy of a two-out hit. Cueto got to first in time to receive a toss from first baseman LaMonte Wade Jr. Cueto couldn’t barehand the ball.

Or get control of it with a swipe of his glove.

But just before Rondon’s foot hit the bag and wrenched away from Cueto, the Giants’ righthander got the ball off a bounce with both his barehand and the glove for the out.

In his six innings, Cueto, once the ire of the Cardinals for his actions with the Cincinnati Reds a lifetime ago, struck out seven and walked one. While the stinging hits against Wainwright came from Crawford, the ones that scarred Cueto’s line came from throughout the Cardinals lineup. Four different Cardinals scored runs against the righthander, but the RBIs were evenly split between the two hitters the Cardinals have yet to see going at the same time — Goldschmidt and Arenado.

“These wins right now — they feel like we can play with anyone, we can beat anyone, we just need the mojo,” Wainwright said. “A couple of games like this will get that mojo swinging in the right direction.”