DUNEDIN, Fla. -- A Yankee belted an important home run over the fence on Wednesday at Dunedin Stadium, one that he will never forget. And it had nothing to do with Alex Rodriguez.

This came off the bat off Brett Gardner, who cracked the second pitch of the Grapefruit League campaign over the wall off Blue Jays left-hander Brett Cecil. It came in the first game attended by his son, Hunter, born in November 2008.

"It'll be a nice story to tell about the first game he's been to," Gardner said. "You never know. I might not hit another one all year."

The 24-year-old Garner is kicking off a spring battle with Melky Cabrera to become New York's Opening Day center fielder. With Hunter and his mom, Jessica, looking on from the stands, Gardner got a leg up on the lineup in what finished as a 6-1 Yankees victory.

"Tough act for Jeet to follow," Yankees manager Joe Girardi said, referring to No. 2 hitter Derek Jeter.

"Obviously, I thought we did a lot of good things offensively. Our guys took their walks, for the most part. Defensively, our pitchers threw strikes. I was happy with what I saw today."

New York's first starter of the Grapefruit League campaign was veteran right-hander Brett Tomko, in camp on a non-roster invitation and vying to make the club as a long reliever and spot starter.

Tomko worked two innings of scoreless, one-hit ball. He was 2-7 with a 6.30 ERA for the Royals and the Padres last season, making 10 starts and 12 relief appearances, and he turns 36 in April.

"If I'm the fill-in-the-blank guy, that's good," Tomko said. "I'm not sure if that's the direction I'm heading toward, but I'm pretty content with everybody. This is the opportunity I was looking for. Coming here and having a chance to make the team and pitch well is definitely a good thing."

While the back end of the Yankees' bullpen remains up for grabs, Girardi said on Wednesday that he is locking in the starting rotation.

CC Sabathia will start the March 6 game vs. the Tigers, beginning a sequence that will see Chien-Ming Wang, A.J. Burnett, Andy Pettitte and Joba Chamberlain start. Girardi said that he anticipates the pattern will hold for the regular season, barring injury.

While it may seem surprising that Burnett is envisioned as New York's third starter, especially after signing a five-year, $82.5 million contract, the idea is that Wang represents a sinkerball style of pitcher to slot in between Sabathia and Burnett.

"I talked to A.J. about it and told him," Girardi said. "He said, 'I'll take the ball whenever you want to give it to me.' He was great."

Girardi has said that he wants to give various looks to opposing clubs during series, which is also why he wanted to keep lefties Pettitte and Sabathia separate. Having Chamberlain as the No. 5 accomplishes that, and Girardi said he anticipated Chamberlain would make approximately 30 starts.

"It's the way it should be, if everything goes according to plan," Girardi said. "There's a lot of things that can take place in Spring Training that would change that."

In other updates, Girardi also said that he expects Hideki Matsui (left knee surgery) to begin running on dirt and possibly appear in a game next week. Mariano Rivera (right shoulder surgery) will begin throwing off a bullpen mound next week as well.