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NEW YORK -- The matchup between first-place teams fizzled with the Yankees' first batted ball.

Nyjer Morgan got twisted up in center field and fell trying to catch Curtis Granderson's routine fly that ended up a run-scoring triple, and New York gave Zack Greinke and the sloppy Milwaukee Brewers a rude welcome back to the Bronx in a 12-2 drubbing Tuesday night.

The Yankees scored twice after Morgan's miss in the first, Nick Swisher hit a three-run homer to cap a five-run second inning and the Brewers never appeared to get comfortable in their first trip to Yankee Stadium since their final year as an American League team in 1997.

"If that ball's caught he's probably out of the inning without any damage," said Mark Teixeira, who homered and had four RBIs. "Good pitchers -- it's nice to get to them early because you don't know if you're going to have any more opportunities."

Greinke (7-3) never recovered from Morgan's slip. The 2009 AL Cy Young winner gave up seven runs in two innings, his shortest outing of the season. Greinke walked three, hit a batter and threw a wild pitch in his shortest outing of the season.

"It was just a real bad game," Greinke said. "I wasn't executing anything, and when I did just a couple of times, they took some good pitches, and I wasn't able to make another good pitch after that. I couldn't pitch any worse than I did."

Gardner scored twice without getting a hit and Teixiera had two RBI grounders to second and a two-run homer for the AL East leaders, winners of 13 of 17. Swisher added an RBI double in the eighth, and Robinson Cano, Jorge Posada and Russell Martin drove in runs for New York.

"I thought our guys did a nice job of moving guys over and not trying to do too much," Yankees manager Joe Girardi said.

Freddy Garcia (7-6) gave up eight hits and two runs in six innings.

Ryan Braun doubled leading off the eighth to extend a career-high hitting streak to 18 games. But the NL Central's first-place team made two baserunning blunders to end innings and were 2 for 11 with runners in scoring position. Milwaukee fell to 15-25 away from home, the worst record among winning teams in the majors.

Greinke got off to a wild start, hitting leadoff batter Gardner with a pitch. Granderson then lofted a seemingly routine fly to center. Morgan, however, turned the wrong way and failed to recover, slipping as he dived back to attempt a catch. Teixeira grounded out to second baseman Rickie Weeks for a 2-0 lead.

"I mean, we played bad. It was a bad game for us," Milwaukee manager Ron Roenicke said. "We got a lot of hits, but it was not a well-played game."

Eduardo Nunez led off the second with a walk, moved to second on a wild pitch, stole third and scored on Teixeira's second RBI groundout to Weeks. Cano had an RBI single before Swisher hit his 10th homer for a 7-0 lead.

Greinke, who gave up five hits, has a 6.75 ERA in 11 games with the Royals and Brewers against the Yankees.

Milwaukee's woes were not limited to defense. Mat Gamel, called up from Triple-A Nashville on Monday, was thrown out 9-2-6 trying to advance to second on Yuniesky Betancourt's sacrifice fly to right in the fourth that made it 7-2. Gamel had an RBI single earlier in the inning.

Corey Hart was easily thrown out at home on a strong throw by Swisher to end the sixth after Gamel singled.

Brewers right-hander Marco Estrada was hit in the left foot by Alex Rodriguez's sharp grounder in the sixth -- one batter after Teixiera homered -- and left after throwing two warmup pitches.

Zach Braddock, called up from Nashville on Monday, relieved and walked his first batter when he brought his hand to his mouth while standing on the rubber with a full count to Cano.

Even Prince Fielder had trouble, apparently getting dirt kicked into his eye when A-Rod beat out the infield single that caromed off Estrada. Fielder danced around in pain for a few moments before rubbing the eye clean.

The Brewers had a chance to take an early lead, but stranded runners on second and third in the first.

With one out, Morgan singled and Braun was hit by a pitch. After Fielder, the NL RBI leader, flied out to left, Morgan and Braun executed a double steal. But Garcia struck out Casey McGehee to end the threat.

Game notes

The only time the teams have met in interleague play was in 2005, in Milwaukee. ... Brewers RHP Takashi Saito (hamstring), on the 60-day DL, could return for the series at Minnesota that starts Friday. ... The Yankees have outscored their opponents in the first two innings 118-66.