So when Ryan Sweeney singled on a ground ball in the ninth inning off Yankees closer Mariano Rivera, the A's had their chance to erase a one-run deficit and avoid both a loss and a series sweep.
But that chance proved to be short-lived.
The A's couldn't capitalize on Sweeney's hit and fell, 2-1, to the Yankees for their second straight one-run loss.
"[These were] just tough games here. A couple of them, we could have won," manager Bob Geren said. "We obviously need to get more offense, there's no doubt. It's tough to win when you get one run."
Bobby Crosby followed Sweeney and hit what seemed to be a sure flyout to right fielder Bobby Abreu, so Sweeney stayed close to first base. Then, in an unusual play, Abreu dropped the ball, but Sweeney was eventually forced out at second base.
"It's so short out there," Geren said. "If you get too far out and he catches it, you're out at first. If it was deeper, a bigger ballpark or something out there, maybe you could get off a little further, but it is very short out there, and the chance of a big league outfielder dropping the ball is slim."
Rajai Davis came in to pinch-run for Crosby, but as he tried to steal second and get himself into scoring position, Yankees catcher Jose Molina sprung up and threw out Davis to end the game.
The loss came despite an impressive performance from starter Justin Duchscherer. The right-hander threw seven innings on a hot and muggy day despite feeling under the weather. He had stayed at the hotel on Saturday afternoon to rest from a viral infection, and the day away seemed to help, as he gave up just two runs on six hits.
"It was a very gutsy, hard-fought performance by him," Geren said. "If he got a couple of runs, we probably would have won the game."
Duchscherer didn't make many mistakes, but Jason Giambi made him pay for a fastball in the sixth inning, knocking a solo home run over the right-field wall to break a 1-1 tie and put the Yankees on top for good.
"Giambi just seems like my nemesis," Duchscherer said. "No matter what I throw at him, he seems to find a way to beat me. It's just frustrating to lose, 2-1, like that."
Sunday's loss marked the 27th time this season the A's lineup has been held to one run or fewer. Though the A's boast one of the best rotations in the league, they have struggled to back up their pitchers with run support.
Oakland continued the trend by combining for just five runs during the three-game series against New York.
"It's kind of the same old story -- the pitchers throw good and the offense isn't doing well," second baseman Mark Ellis said. "We're striking out a lot, I know that. I think guys are aware of it, though, and I think that just adds to the problem. So if you go up there and just try to have good at-bats, it will probably take care of itself."
The bats never quite warmed up for Oakland. Sweeney connected on two hits off Pettitte, but the rest of the lineup couldn't get into a rhythm.
"He pitched like a veteran that was on top of his game, he really did," Geren said of Pettitte. "He pitched inside enough to keep the players from leaning out over the plate."
Sweeney went 2-for-4, including an RBI single to give Oakland its lone run, and he showed off his defensive skills when he threw out Alex Rodriguez at home plate from right field in the first inning. Sweeney scooped up a line drive by Robinson Cano and sent the ball flying to catcher Rob Bowen for the out.
But despite Sweeney's performance, the A's couldn't keep the Yankees off the scoreboard for long. Derek Jeter came in from third base to open the scoring in the third inning when Rodriguez hit a sacrifice fly to right field.
Geren argued that Jeter left third before the ball was caught, but the ruling stood, and the Yankees took a 1-0 advantage.
"From my level, I thought he left early," Geren said. "But I don't get the benefit of a replay, and neither does the umpire."
For the second day in a row, the Yankees outlasted the A's, but it wasn't because of a lack of effort on Oakland's part, and Geren continues to be impressed with his team's determination and drive, even if the results don't always show it.
"They work hard all the way to the last out," he said. "I give them a lot of credit for fighting all the way to the end, all the time. It's a good feeling. The guys never stop playing."
Samantha Newman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.