ANAHEIM -- The Yankees' chances at October baseball may have been reduced to a sliver, but Alfredo Aceves offered plenty of promise for those willing to look ahead to the organization's future.

Making his first Major League start and just his third big league appearance, Aceves did not disappoint, hurling seven strong innings. Alex Rodriguez went deep and Johnny Damon homered twice to help the Yankees secure a 7-1 victory on Tuesday at Angel Stadium.

"It's like another step," Aceves said. "Now that I'm here, I'm not thinking my past or my future. I just leave it be. That's not part of my job. My job is to hold the other teams and play good baseball."

A 25-year-old who was acquired in a $450,000 transaction before this season from Monterrey of the Mexican League, Aceves said he left 27 passes for family and friends, some of them coming from as far away as Mexico.

With his loved ones scattered down the left-field line and in the sections above the dugout, the right-hander made sure that the trip was worth it, limiting the Angels to one run and five hits in an 89-pitch effort that earned his first Major League victory.

"He told me he was going to give me seven [innings], so I guess I have to listen to him more often," Girardi said. "He faced a tough lineup tonight but he threw a lot of strikes, he was ahead in the count all day and he was putting the ball where he wanted to."

Showing more polish than an average rookie, Aceves picked up his defense after a potentially costly Derek Jeter error in the fourth inning by inducing Torii Hunter to hit into an inning-ending double play, and working out of a second-and-third situation in the sixth by allowing only one run to score.

"To be able to come from A-ball all the way up tells you something about what's inside of him," Girardi said. "The kid has a lot of heart. Obviously he's not afraid to throw strikes and go after hitters, and that's a good thing. So far he hasn't been fazed by his surroundings, because that's as tough as it gets."

Aceves' father, Alfredo Aceves Sr., was a power-hitting first baseman for four years in the Mexican League, playing for Leones de Yucatan. Watching from the grandstands at Angel Stadium, Aceves Sr. said in Spanish that he was more nervous than his son appeared.

"Big moment for me," Aceves Sr. said. "I taught them to play the game hard. His work and confidence, he confronted a team with big bats -- the biggest, strongest team, which is the Angels."

A memorable evening for Aceves' family opened with a historic note, as Jeter's first-inning single moved him past Babe Ruth's 2,518 career hits for second place on the Yankees' all-time list. Jeter finished 2-for-4 with a run scored, giving him 2,520 as play completed.

"It sounds funny, to be honest with you," Jeter said. "Anytime you're mentioned in the same sentence with players like that, it feels good. I was a Yankee fan growing up so I'm well aware of all the history. I think it's something that maybe I'll get an opportunity to reflect on."

Xavier Nady put New York on the board with a second-inning double off Angels starter Ervin Santana, and Rodriguez's three-run homer in the sixth inning opened up some breathing room for Aceves, a no-doubt shot to right-center that followed Gary Matthews Jr.'s three-base error on a Jeter ball and a walk to Bobby Abreu.

The blast was A-Rod's 206th homer as a Yankee, passing Dave Winfield and Jeter while tying Jason Giambi for 10th place on the club's all-time list.

Damon added a two-run homer on Santana's final pitch, closing out his line at six runs -- five earned -- on nine hits over 6 1/3 innings, walking one and fanning six.

"I love when we get that from them," Girardi said. "Johnny and Alex are a big part of our lineup. When we get big nights from them, we usually win."

Damon also homered in the eighth off Justin Speier to extend the lead, posting his second multi-homer game of the season and the 12th of his career. The victory improved the Yankees to 5-4 on a 10-game, four-city road trip that concludes on Wednesday afternoon.

"There's been a lot of guys in here struggling lately," Damon said. "It's that time of the season. We really need to go down there and bear down as much as we can."