Righty Jesse Chavez was superb in six innings of one-run ball, and power resurfaced from a lineup that got a pair of three-run homers from Derek Norris and Coco Crisp, who combined to go 5-for-9.
"It's good to see," manager Bob Melvin said. "We haven't been swinging the bats as well as we were earlier, but two big three-run homers today gets you off to a good start."
The A's love their homers, but they had gotten just one long ball in the previous five games after a season-best streak of 16 consecutive games with at least one.
"Ever since I've been here, we've been built around the long ball," Norris said. "We obviously made ourselves a little more well-rounded over the last couple years, but when we're hitting homers, we're winning. That's the bottom line."
Five of the catcher's seven homers this year have come with at least two men on base, including two on Mother's Day.
So even though Norris already made his morning call to dad on this Father's Day, the two will surely speak again before night's end.
"I'm sure he'll be like, 'Why didn't you hit two?'" said Norris, smiling.
The catcher not only got the A's on the board with a three-run homer in the first, but he also collected a single and a double -- falling a triple shy of the cycle.
Jeter, meanwhile, notched a double and an RBI, and scored a run, but the A's ruled the day, improving to 42-27 in advance of a three-game meeting with the Rangers. It's Oakland's best record after 69 games since going 44-25 in 1990.
The A's also let out a sigh of relief in watching Josh Donaldson snap a career-worst 0-for-33 slump, with the third baseman, bumped to the sixth spot of the lineup, squeaking out a slow RBI grounder through the right side in a four-run fourth inning.
Yankees starter Vidal Nuno didn't get an out in the fourth frame, boarding two batters before being pulled in favor of righty Jose Ramirez, who loaded the bases and hit Craig Gentry in the head with a curveball. A's trainers rushed from the dugout, but Gentry was deemed OK to take his base, at which point Yoenis Cespedes notched a two-run base hit.
Nuno, in just three-plus innings, was charged with eight runs, and Ramirez was ruffled for two. Chavez fared much better.
The righty didn't walk a batter and allowed just one run on five hits with four strikeouts in six impressive innings, lowering his ERA to 2.93.
"That's the biggest thing, not to walk anyone," said Chavez, "and not to give up the two-strike hits that had been my Achilles' heel the last four or five starts."
"Today was, I thought, similar to what we were seeing real early in the season," Melvin said. "You could tell right away he was on it pretty good, cutter to both sides of the plate, good curveball to create a gap between the hard stuff and the offspeed stuff, threw a few good changeups
"It's not like he was pitching poorly, but this is the type of outing we were seeing earlier in the year when he was really knifing through teams and cutting through them very quickly."
A's relievers Ryan Cook and Jim Johnson combined to allow four late-inning runs, but their teammates had done enough in the early going to offset some shaky relieving.
In all, the A's rung up 12 hits, with five starters -- Norris, Crisp, Gentry, Cespedes and Kyle Blanks -- enjoying multi-hit days.
"It was nice to get the bats going," Norris said. "As a whole, we've been in a little bit of a slump, and putting together some consecutive knocks there, put some runs across the board, it was good to break out today."