Scutaro has ended games seven times with hits, once with a home run, in his three seasons with the A's.
"I'm not a big RBI guy," he said. "I focus just to see the ball and try to get a good pitch."
Scutaro was in the lineup because Bobby Crosby suffered a deep cut on his left index finger on Monday night. He's been a valuable player for the A's since they claimed him on waivers from the New York Mets in 2003.
"It's good timing I guess," Scutaro said. "I never faced the guy before, so I wanted to see a pitch and see what kind of movement he had. I was looking for a pitch and I hit it good."
The Yankees took a 3-2 lead in the top of the sixth against A's starter Rich Harden, who lasted 5 2/3 innings. Justin Duchscherer got the final out of the inning and two other relief pitchers held the Yankees until Scutaro delivered his big hit.
Harden tired in the sixth and blamed a 30-pitch first-inning for his troubles.
"That's not what I wanted to do in my first start and my first inning," Harden said. "I was a little too excited and I needed to get through that. But that's what killed me later in the game, making too many pitches in the first. I had nothing left at the end of the game."
Duchscherer, Joe Kennedy and Huston Street, who got the win after a scoreless ninth, had plenty to spare to keep the A's in it.
"They all pitched well and made good pitches," A's catcher Jason Kendall said. "Last night was a little disappointing but we came back and Scutaro got the big hit."
A key to winning was shutting down Yankees' cleanup hitter Alex Rodriguez, who stranded five runners in scoring position on the night.
"When you have so many different opportunities and can't deliver the big hit, you get an 'L,'" Rodriguez said. "That was the big difference between yesterday and today. Yesterday we delivered the big blow."
Eric Chavez tied the game at 3 in the sixth with his first home run of the season, a blast into the right field bleachers.
The A's strung together four consecutive hits to produce two runs in the third and take a 2-1 edge. Swisher hit a home run with one out. Scutaro and Ellis singled, and Mark Kotsay singled home Scutaro.
Scott Proctor walked Bradley to open the ninth and Kendall bunted him over to second. He walked Swisher to set up Scutaro's drive off the left field wall that ended the game.
Harden made his first start since last Aug. 19, and wound up with a no-decision after allowing three runs on seven hits with four walks and four strikeouts.
"Every time I gave up a run, we came back and got a run. That was huge," Harden said. "I didn't have my best stuff. I was making pitches with my fastball. I was having a little trouble with my off speed pitches. Either they weren't good enough to swing at or they were too good, and I left them up."
Harden spent two separate stints on the disabled list last year due to a strained left oblique muscle and a right lat strain. He was also slowed by food poisoning in Spring Training and was limited to three starts in 'A' games. He also pitched a simulated game and against Triple-A Sacramento.
He showed no ill effects and managed to pitch his way out of early trouble. Johnny Damon walked and Derek Jeter doubled to start the game but Harden came back to strike out Gary Sheffield, Rodriguez and Jason Giambi.
Sheffield came back to double home a run in the third, and Jorge Posada drove in runs in the fourth and sixth.