Robinson Cano's error in the eighth inning allowed Milton Bradley to score the game-winner, capping a night in which Bradley also drove in three runs for Oakland.
Derek Jeter misplayed a potential inning-ending double-play ball in the fourth, helping the A's start a three-run rally.
Hideki Matsui and Gary Sheffield each went deep for the Yankees, but Chien-Ming Wang was unable to protect an early four-run lead, allowing four runs -- two earned -- over 4 2/3 innings in his first start of the season.
"Everyone keeps talking about our offense, but that doesn't win games; pitching and defense does," Jeter said. "We're not always going to hit every game."
Matsui put the Yankees on the board in the second, crushing a solo home run, his second of the year, to center field against starter Dan Haren.
One inning later, Haren ran into more trouble, putting runners on the corners to start the inning after Cano doubled and Johnny Damon singled. Haren struck out Jeter, but Sheffield drilled a 2-2 pitch to left field, keeping it fair as he tucked it inside the foul pole for his first homer of 2005.
The homer was No. 450 for Sheffield, pushing him past Frank Thomas and Jeff Bagwell for 27th on the all-time list.
Wang posted zeros in each of the first three innings, but the young sinkerballer gave up three runs in the fourth. The inning could have been prevented had Jeter been able to field a one-out grounder hit by Thomas, as a double play would have ended the frame.
Instead, Wang walked Dan Johnson to load the bases, then Bradley lined a single to left field, plating a pair of runs. Jason Kendall's RBI fielder's choice cut the lead to 4-3.
"I have to make that play," Jeter said. "Wang was pitching well -- he was in a groove -- but after that mistake, it took him out of it. If I make that play, we're out of the inning. They really capitalized on it."
Oakland tied the game in the fifth, using two singles and two walks -- the last of which was a bases-loaded free pass to Bradley -- to knot the game at 4.
With the bases still juiced, Torre replaced Wang with Tanyon Sturtze, who got Jay Payton to pop out to Jason Giambi, stranding all three runners.
"Our pitching staff did a good job, but we made a couple of mistakes that cost us a few runs. You can't do that, especially against a team with a pitching staff like Oakland's."
-- Derek Jeter
Jaret Wright made his season debut, coming out of the bullpen to start the sixth. It marked the first relief appearance for Wright since September 2003, but he had no trouble adapting to his new role, retiring six of the first seven batters he faced.
But Haren settled in after giving up Sheffield's blast in the third, retiring 10 of the final 11 batters he faced. Haren left after six innings, charged with four runs.
"I give Haren a lot of credit," Torre said. "We scored four runs and he didn't rattle. He pretty much frustrated us."
Bradley continued to be a thorn in the Yankees' side, belting a triple just past Damon's outstretched arm in center to start the eighth.
"I couldn't get back fast enough," said Damon. "It just beat me. I couldn't get as high as I wanted to. I have to make that catch."
"It looked like he had a pretty good jump on the ball," Torre said. "It just kept going."
With the infield drawn in and the go-ahead run just 90 feet from home plate, Payton hit a hard grounder at Cano, who was in perfect position to field it. But the second baseman took a quick look to see if Bradley was running, taking his eye off the ball for a split-second. It was enough to cause him to mishandle the grounder, allowing Bradley to score on the error.
"I'm not perfect," Cano said. "It's something that's going to happen in the game. I don't want it to happen, but I'm human. I'm going to make mistakes. ... If I don't make that mistake, it's a different story."
The A's cemented the victory with four more runs in the inning against Wright (0-1) and Kyle Farnsworth, the big blow coming on Thomas' three-run double, which boosted the lead to five runs.
"Pitching wins, but you have to play defense behind that pitching," Jeter said. "Our pitching staff did a good job, but we made a couple of mistakes that cost us a few runs. You can't do that, especially against a team with a pitching staff like Oakland's."
"It's nothing we have to work on," Torre said. "This ballclub works hard; it's just something that happens. We just have to turn the page."