Better at-bats and more consistency from the bullpen.
It's been an impressive first half nonetheless.
"Trust me, I'm happy with the way we're playing and how hard our guys are playing, but I still think we can get better," Girardi said.
Francisco Cervelli added an RBI single as New York gave Javier Vazquez (7-7) all the offense he needed to end a three-start winless stretch. The right-hander outdueled Ben Sheets, Oakland's $10 million man who has just one win over his last 11 outings.
The Yankees increased their lead in the AL East to two games over Tampa Bay, which beat Boston to drop the Red Sox to 2 1/2 games back.
Vazquez made his 400th career start, the seventh pitcher to reach the milestone while with the Yankees, and helped New York win for the eighth time in its last 11 road games.
He, too, insists New York can improve.
Vazquez sure liked the way the defense played behind him. He was aided by back-to-back diving catches by Granderson in center and Colin Curtis in right field to end the seventh.
"That was unbelievable in the seventh inning those two catches by Grandy and Colin," Vazquez said. "We're playing good. We still feel we can play better. Hopefully it says something that we're 20 games over."
Nick Swisher doubled and singled against his former club, still making a push for a last-minute All-Star spot. This is the Yankees' second trip to Oakland this year, kicking off a seven-game road trip that also features four games at Seattle before the All-Star break -- New York's last West Coast swing of the season.
Teixeira's homer was his 14th overall and sixth in 25 games since June 8.
The A's lost for only the third time in their last 10 games. New York is 7-3 at Oakland since 2008.
Vazquez allowed three hits and one run, struck out two and walked two in seven strong innings. Joba Chamberlain pitched a perfect eighth with two strikeouts and Mariano Rivera finished for his 19th save in 21 chances as New York retired the final 15 batters in order.
Sheets (3-8), who lost to the Yankees back on April 21, struck out four and didn't walk a batter in a season-high 7 1/3 innings -- lasting seven innings for only the third time in 18 starts this year. He gave up eight hits and three runs.
He went further than seven innings for the first time since Sept. 6, 2008, for Milwaukee in a shutout of San Diego.
The right-hander, who didn't pitch in 2009 while recovering from reconstructive elbow surgery, has given up at least three extra base hits in each of his last eight starts.
"The deeper you get the more you expect to go back out there," Sheets said. "I knew getting deep would be a process. I didn't realize it would be this difficult. I'm starting to feel better toward the end of games, which is good. I think my stuff's starting to get better as opposed to earlier in the year when it was decreasing a lot. I'm pleased with that. I have to find a way to come out of the gate, it's something I've struggled with my whole career."
He had a 10-pitch, 1-2-3 inning in the first and had retired the first five batters in order on 13 pitches before the Yankees got to him with Swisher's double, the triple to Granderson and Cervelli's single before the second inning ended.
"Any time you can come up and get hits there it's big," Granderson said. "It's difficult to do."
Kevin Kouzmanoff's single in the fourth for the A's snapped his 0-for-30 skid.
The 38-year-old Pettitte was added to the team Monday because he was next in line in voting by AL players. Buchholz was placed on the 15-day disabled list Monday with a strained left hamstring.
Girardi said he hasn't decided who he will pick to replace Oakland RHP Trevor Cahill on the AL All-Star team. Cahill is scheduled to pitch for the A's on Sunday, two days before the midsummer classic and therefore won't be available to pitch. He will still attend the festivities. ... The A's are selling 'Get Off My Mound' T-shirts, a reference to the April 22 game here between the two teams when Alex Rodriguez jogged over the pitching mound while heading back to first base on a foul ball, a move that infuriated Oakland pitcher Dallas Braden. Braden, who is on the disabled list, won't be pitching in this three-game series. Girardi's playful suggestion: have both players autograph some of the shirts for auction. A's players have expressed frustration in the club's marketing department in making the shirts. ... A's LHP Brett Anderson (elbow) threw 20 pitches during a simulated inning in Phoenix and could pitch in a rehab game on Friday. ... It was just 58 degrees at first pitch.