Andruw Jones homered and Mark Teixeira doubled home a run to provide the offense, and Rafael Soriano pitched a scoreless ninth inning for his fifth save as the Yankees squeezed out a tight victory to extend their season-high winning streak to five games.
"Everyone has to win those close games, or you're not going to get into the playoffs," Teixeira said. "You're not going to have enough wins, so it's really important for us to win those close ones."
Oakland has proved to be an appealing road destination for the Yankees, who have won eight straight at the Coliseum dating back to 2010. New York returns to the Bay Area for a four-game series in July.
"We're playing better," Yankees manager Joe Girardi said. "I still don't think we've hit on all cylinders. I think we can even get better, but we're playing better and winning games. That's the most important thing."
Derek Jeter notched another milestone in the win, singling in the first inning to pass George Brett on baseball's all-time hits list with 3,155.
"It's humbling when you hear those names, because any name you pass, there's a Hall of Fame guy," Jeter said. "It's pretty special."
Kuroda has been more inconsistent than the Yankees hoped, entering the start 0-4 with a 6.23 ERA in four starts away from Yankee Stadium, but he appeared plenty capable of handling a punchless Athletics lineup.
Leaning on an excellent sinker and slider, Kuroda faced the minimum into the fifth inning and did not permit a baserunner to reach second base until the seventh inning.
"I thought those were the two big pitches for him, whether he was throwing it away from lefties or away from righties," Girardi said. "I thought he did a really good job of getting back into counts with his slider and then using his sinker effectively."
Kuroda navigated a two-on, one-out jam in the seventh by striking out Kila Ka'aihue and getting Josh Donaldson to fly out, finishing allowing four hits, walking one and striking out three.
"He just got a little rushed," catcher Chris Stewart said. "Once he was able to take a breath and realize his stuff was good enough, he made some really big pitches and got out of a big jam."
A's manager Bob Melvin said that Oakland's offense was pressing as they dropped their fifth straight game, but he offered Kuroda credit as well.
"You certainly can't just say it's all us when a guy throws eight innings of shutout ball," Melvin said.
The Yankees are winless this season in games in which they have not homered, faring 0-10 in such contests, and Jones improved their chances for victory with a second-inning solo blast off A's starter Tommy Milone.
"I've never seen the guy, so all I know is from videos," Jones said. "Watching the video, he likes to throw the first pitch up and away, and he just made a little mistake out over the plate. I just had a good swing."
Making his first career start against the Yankees, Milone was able to pitch out of trouble as New York's problems with runners in scoring position made another appearance.
Milone left the bases loaded in the first inning by getting Robinson Cano and Nick Swisher to pop out, foreshadowing an afternoon that would see the Yankees finish 1-for-11 with runners in scoring position.
"Their young left-hander threw a very good game today," Girardi said. "He's got an outstanding changeup that he used at any time. We had some chances early, and he really settled down."
Milone finished allowing two runs and eight hits in 6 2/3 innings, losing for the first time in five home starts this season.
Teixeira was the star of the weekend, picking up six extra-base hits in the sweep, including three home runs. Coughing less and slugging more, Teixeira is 10-for-23 (.435) with nine RBIs in his last six games.
"I've been waiting for that hot streak, and I've found it the past few days," Teixeira said. "Sometimes that's the name of the game. It's just getting hot, and as a team we're winning some games, which is great."