New York Yankees first baseman Mark Teixeira (25) watches his...

New York Yankees first baseman Mark Teixeira (25) watches his two-run home run in the bottom of the sixth inning against the Milwaukee Brewers at Yankee Stadium. (June 28, 2011) Credit: Christopher Pasatieri

The Yankees gave Freddy Garcia everything he needed.

Before the righthander stepped onto the mound to face Milwaukee in the third inning Tuesday night, he had a seven-run cushion with which to work. That kind of run support -- typically reserved for ace CC Sabathia -- was more than enough for Garcia, who cruised in a 12-2 win over the Brewers in the series opener at the Stadium.

With Boston's loss, the Yankees (46-31) have a 1½-game lead over the Red Sox in the American League East.

Nick Swisher belted his 10th home run in a five-run, second-inning outburst for the Yankees, who have outscored opponents 118-66 in the first two innings. The game was well out of reach by the time Mark Teixeira drilled his 24th home run over the rightfield wall, a two-run shot in the sixth. Teixeira is tied with Toronto's Jose Bautista for the major-league lead in homers.

The Yankees totaled 10 hits -- one fewer than the NL Central-leading Brewers, who dropped to 15-24 on the road.

Former Cy Young winner Zack Greinke (7-3) was yanked after just two innings, allowing seven runs and five hits in his shortest outing of the season. He walked three, struck out none, hit a batter and threw just 56 pitches (32 for strikes).

After taking a 2-0 lead on an RBI triple by Curtis Granderson and an RBI groundout by Teixeira in the first, the Yankees scored five more in the second. Eduardo Nuñez singled, stole second and third, and scored on a groundout by Teixeira, who totaled four RBIs. Robinson Cano drove in Brett Gardner with a single to make the score 4-0 before Swisher (2-for-4) crushed a three-run homer to right-center.

"The first inning messed him up mentally," Milwaukee manager Ron Roenicke said of Greinke's uncharacteristic night.

Garcia (7-6), meanwhile, had little trouble against the Brewers. He escaped a first-inning jam, in which he gave up a single to Nyjer Morgan before hitting Ryan Braun with a pitch. Both runners advanced on a double steal with two outs, but Garcia struck out Casey McGehee to end the inning.

With their starting rotation in flux -- and the status of Bartolo Colon and Phil Hughes still left to sort out -- Garcia has provided the Yankees with some much-needed stability. The righthander, signed to a minor-league contract worth $1.5 million, is 31-13 in the month of June.

Asked if he's surprised by his start, Garcia said: "Not really . . . If I'm 100 percent, I can go out there and pitch my game."

Tuesday night was the first time since May 25 that Garcia (eight hits, one strikeout) didn't walk a batter.

The Brewers (44-36) scored two runs in the fourth and seemed poised to strike again in the sixth after Corey Hart doubled off Garcia with two outs and Mat Gamel singled to rightfield. Swisher, however, fielded the ball as Hart lumbered around third and launched a low line drive to Russell Martin, who easily tagged out the runner at home to end the inning.

As the Yankees headed to the dugout, Martin couldn't help but rib his teammate. Swisher said: "He said, 'Man, you want the ball? Cause I bet that doesn't happen very often.' I did, I took the ball.

"I just wanted to do my best to keep the ball down, got a good skip and when you put it in those mini clamps that Russ has for hands, it's not going anywhere," added Swisher, who said relievers David Robertson and Boone Logan have helped tailor his cutoff throws so they're not as high and wild.

"I'm trying to take a little more pride in the defensive end of things," said the rightfielder, who drove in four runs and has 22 RBIs and seven home runs this month.

The Yankees tacked on four runs in the sixth on Teixeira's homer, an RBI single by Jorge Posada and a fielder's choice that allowed Cano to score. This is just the second series between the teams since the Brewers became a National League team in 1998 and the first visit for Milwaukee as an NL team to Yankee Stadium.

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