The right-hander was able to earn his seventh win thanks to third baseman Brandon Inge. The veteran promised the rookie that he would "get him one" before he went to lead off the bottom of the eighth, and he did, clubbing the first pitch he saw from Yankees starter Phil Hughes out to right-center to break the 1-1 tie.
But it was another rookie in Sean Doolittle who promptly stole the show.
Doolittle's stunning story is well documented. Originally a position player, he didn't begin pitching professionally until instructional league last year but shot up three Minor League levels this season and has a 1.86 ERA for the A's.
The left-hander allowed a leadoff single to Alex Rodriguez in the ninth but proceeded to strike out Robinson Cano, Mark Teixeira and Andruw Jones to pick up his first career save.
"That was fun. That was right up there with my debut," Doolittle said. "I think part of it was the Yankees, it was a save situation, the guys that I was going to face. It was a rush.
"Looking back on where I've been and where I am now, it makes it that much more special."
"That's a goose bump-type of thing," A's manager Bob Melvin added.
It was only the latest chapter in what is quickly becoming a remarkable season for Oakland. A nine-game losing streak in late May and early June could very well have submarined the team's season.
But the club has developed an impressive resiliency, and the players, to a man, are always talking about their strong belief in their abilities as a group.
That's manifested itself in the A's recent run, which has seen them win eight of their last nine games -- with seemingly every one of them a walk-off or late-inning victory -- and claim the Majors' best record in July at 13-2.
On Saturday, that resiliency was first evidenced by Yoenis Cespedes tying the game with his 13th home run in the bottom of the fourth, right after the Yankees went ahead in the top of the inning, and later by Inge's long ball.
Cespedes' blast extended the rookie's career-high hitting streak to nine games.
Oakland's been successful mostly thanks to its pitching staff, which came into Saturday's game with the lowest ERA (3.40) in the American League. In the team's last four games, the pitchers have held the powerful Rangers and Yankees to a combined nine runs.
"Our offense, we're getting a lot of credit for the walk-offs and everything. The part of our team that's getting overlooked a little bit is absolutely our pitching staff," Inge said. "They have been incredible. They've been really, honestly, the glue that's held us together through this whole thing. It's amazing that they're doing such a good job and kind of flying under the radar."
The Yankees had scored at least three runs in 43 straight games before Friday, but managed to plate just three runs combined in the last two contests. And it's been three rookie starters who've led the impressive effort in the first three games of the series.
Parker was just the latest, and he finished with a flourish, allowing one baserunner after the fourth inning and striking out two of the last three hitters he faced.
"Great changeup. Really good changeup," Yankees manager Joe Girardi said. "He can throw it any time; We saw some 3-2 that he threw for strikes, he ended up walking [Curtis Granderson] on one. They've thrown strikes, that's the big thing. They haven't walked people."
One need look no further than Saturday night's game to see just how bright the A's future could be, what with their bevy of young players producing on a nightly basis.
But the present is plenty bright, too. With the win, Oakland moved into a tie with the Orioles and White Sox for the second Wild Card spot and sits just a half-game behind the Angels for the first Wild Card.
"We prepare and do what we need to do against [other teams], but this is our family right here," Inge said. "We do what we do and everything else is going to take care of itself. I think that's why we're not getting caught up in anything. Just playing and having fun."