Daniel Hudson and rookie Ben Casparius with one apiece extended the Dodgers staff’s scoreless innings streak to 33, which includes the final 24 innings of the San Diego series. That matches the best postseason stretch in major league history, and there’s a back story here.

The 1966 Baltimore Orioles also recorded 33 scoreless innings in a row ... in the World Series ... against the Koufax-Drysdale Dodgers, in a four-game sweep. Those Dodgers, notoriously weak offensively, were eighth out of 10 NL teams in runs scored with 606, and didn’t score in that World Series after the third inning of Game 1.

So the Dodgers franchise now has a chance for some psychic payback, 58 seasons later. A scoreless first inning this afternoon will do it, and if nothing else it’ll mean something to those who were around all those years ago.

A few more shutout innings — a bunch more, actually — will be useful in terms of the ultimate goal, as articulated on Dodger Stadium’s ribbon board after Sunday’s game: “7 wins to go.”

How impressive/important were those seven innings from Flaherty?

“It was just a pitching clinic,” manager Dave Roberts said. “I thought he did a great job of filling up the strike zone with his complete mix. Used his fastball when he needed to. Just minimized damage. And once we caught a lead, he did a great job of just going after those guys and attacking.

“And for us to get seven innings in a long series was huge.”

Flaherty mixed his pitches effectively, got whiffs or called strikes on 28 percent of his pitches and only had one runner in scoring position. And he got help in the fifth from Kiké Hernández, playing center field, whose fake throw to third on a bloop single to left center by Jose Iglesias deked lead runner Jesse Winker into confusion, and led to his being thrown out at third and defusing a potential threat.

The break the high-leverage bullpen guys received can’t be overstated, since Roberts confirmed what was expected: This afternoon’s Game 2 will be a bullpen game, opener TBA.

For Flaherty himself, that kind of performance in this ballpark absolutely resonated. The kid from Harvard-Westlake, who watched games here and pitched (and won) here in a CIF Southern Section final in 2013 — with, incidentally, a complete-game shutout — came up with the performance a kid dreams about, in a big game, for his hometown team, with his mother in the stands.

“I saw some family out there when I was warming up and I had gone to games here with them before, so ... (it) just kind of lets you relax a little bit,” Flaherty said. “At least that was the way it was for me tonight.

“This game is a lot of fun and I’ve been lucky to do it since I was a little kid. I’m still lucky to be able to do it today and be put in these positions, which is why I kind of try to describe these games as fun. As high pressure as they get, I just tell the guys it’s going to be fun. We’ve got to remember that sometimes.”

And walking off the mound after the seventh inning with a smile, getting a big hug from his manager and then coming back out to embrace his mom ... yeah, that’s fun, all right. That’s the stuff dreams are made of.

“I told my mom I was going to come out and just give her a hug, the way we’ve been able to,” he added. “Just instead of waiting to meet her underneath or whatnot, if I can just go out give her a hug, tell her thanks for being there and supporting me. It’s always important.”

As important as the deadline trade for Flaherty seemed to be at the time, it has turned out to be exponentially larger as injuries have thinned the Dodgers rotation. And when they needed him to step up and pitch like an ace in a crucial situation, he did.

“I think we’re getting Jack at the perfect time as far as he’s a veteran player, he’s been through a lot, highs, lows, and found his way back,” Roberts said. “This is certainly a childhood dream for him and his family. We just knew that you vet a guy and you just feel that he can handle this market, handle pitching in a playoff game, starting a playoff game. That wasn’t really a surprise for us. ... The moment just isn’t going to get too big for Jack.”

If the plan works as intended, there will be more big, critical moments to come in these playoffs for the hometown guy.

jalexander@scng.com