It would make for a great story to say Mike Yastrzemski had a premonition of the game-tying home run in the ninth inning that made an 8-5, 10-inning win for the Giants possible against the St. Louis Cardinals at Busch Stadium.

It would also be the reverse of the mindset Yastrzemski actually took to the plate against St. Louis closer Giovanny Gallegos with a 2-2 count and a 5-3 deficit.

“Honestly, the thought process is I’ve struck out plenty of times in my life and one more doesn’t change anything,” Yastrzemski told reporters after the Giants won for the 11th time in their past 13 games on the road. “There’s a calmness in that, not worrying about the fear of failure, because it’s already happened before, so it’s not something that really crosses my mind.”

Instead of striking out, Yastrzemski delivered a 417-foot home run that tied the score, his eighth homer of the season and second in two days. Then in the 10th, the Giants got run-scoring singles from Thairo Estrada, Wilmer Flores and LaMonte Wade Jr. against Steven Matz to take a three-run lead.

All that was left was for Camilo Doval to work through a ninth inning that included strikeouts of longtime Giant killers Paul Goldschmidt and Nolan Arenado for his 19th save as the Giants improved to 36-32 and are four games over .500 for the first time this season.

Yastrzemski also delivered a run-scoring single in the seventh that got the Giants within 5-3.

“There’s no one we’d rather have up there in those kinds of moments because his heartbeat is so slow,” Giants manager Gabe Kapler said. “Nothing’s going to be too big for him and he’s going to get a good swing.”

Until Yastrzemski’s home run, it looked as if letting the Cardinals off the hook in what could have been an explosive first inning was going to cost them the game on the day Luis Matos made his major league debut.

With the 21-year-old Matos getting a single on his first swing, the Giants scored twice in the first but could have had much more with St. Louis starter Jordan Montgomery getting three outs with the bases loaded with just the two runs scoring.

Montgomery then went into cruise control, at one point retiring 16 straight hitters.

Giants starter Anthony DeSclafani, meanwhile, gave up a second-inning grand slam to Tommy Edman and a run-scoring single to Jordan Walker in the third, departing the game having thrown only those three innings and needing 78 pitches to get that far.

Fortunately, for the Giants, the bullpen took over and shut down St. Louis the rest of the way. Jakob Junis (three innings), Taylor Rogers (one inning), Ryan Walker (one inning), Tyler Rogers (one inning) and finally Doval finished off St. Louis, which fell to 27-42.

It was the first sweep for the Giants in St. Louis since 1998.

“Really impressive work,” Kapler said. “I thought Rog was especially tough — both of them, actually. Camilo came up and had to face the challenging part of their lineup. It’s hard to see Goldie and Arenado come to the plate consistently. Those guys are so dangerous.”

Tyler Rogers got his first win after four defeats with his scoreless ninth.

Besides the 10th-inning single, it was Wade who set the table for Yastrzemski’s ninth inning home run by drawing an eight pitch walk off Matz, whose record fell to 0-7.

As nice as it is to score two runs in the first inning, the Giants couldn’t help but feel they should have come away with more.

Austin Slater opened with a single, with Matos hitting his first-ever major league pitch for a ground ball single to left and Estrada hitting a single for a 1-0 lead. Flores walked to load the bases, with Patrick Bailey driving in a second run with a single.

The bases were still loaded and no one was out, but Montgomery avoided the huge inning by getting Wade to ground into a force play at the plate and then retire Casey Schmitt on a ground ball double play to end the inning.

After striking out the side in the first inning, DeSclafani ran into instant trouble in the second with Nolan Arenado leading off with a single. He struck out Jordan Walker, then gave up consecutive singles to Dylan Carlson and Paul DeJong to load the bases.

DeSclafani then struck out Andrew Knizner and worked the count to 2-2 on Edman in the No. 9 hole. However, DeSclafani served up a center cut fastball and Edman hit it out to right field to give the Cardinals a 4-2 lead.

The Cardinals added another run in the third on Walker’s run scoring single, and after three innings DeSclafani, in one of the strangest pitching lines you’ll ever see, had given up seven hits and five earned runs, but struck out seven with just one walk.

“It’s kind of weird. I’m not a big strikeout guy, but I had a lot today,” DeSclafani said. “I ran a lot of deep counts. ... I’m not controlling the things I can control, which is throwing a lot of good quality strikes and getting weak contact.”

The Giants take today off before a three-game series at Dodger Stadium against their National League West rivals. They will do so in a very good mood.

“We’ve got a lot of young life that’s come up and played really well and stepped right in and filled some positions because of injuries,” Yastrzemski told NBC Sports Bay Area. “Obviously, there’s a ton of value in that. ... We were kind of getting in a lull, kind of letting games (slip) away from us. We talked about staying in the game no matter what happens and to keep fighting until the last out.”