Rodriguez hit his first homer, a towering drive over the scoreboard in left in the third off Rick Porcello, who was charged with four runs -- one earned -- and four hits over three innings.
"That one felt really good just because it wasn't an everyday home run," Rodriguez said. "As you get closer to Opening Day, obviously, you've got to make sure you hone in on your swing, and so far so good."
Sabathia, lined up to pitch the regular season opener April 4 at Boston, gave up four hits, two walks and struck out eight. He left in the sixth with two on -- both reaching on walks -- and one out. One of the baserunners scored later in the inning.
"My offspeed pitches were good," Sabathia said. "Changeup was really good. Got some swings and misses on my cutter. Fastball was good, too. I was pleased with today."
Yankees shortstop Derek Jeter, who had a two-run single in the second, was in the lineup and said his throwing hand is fine. He flexed the hand several times after diving for a ball in the fourth inning Thursday night but remained in the game.
Porcello had his string of 10 consecutive shutout innings end in the second when the Yankees scored three unearned runs with two outs.
"Porcello didn't get his breaking ball going until the last inning," Tigers manager Jim Leyland said. "Command problems second inning, but he's fine."
The Tigers have pitching issues to address over the final two weeks of spring training. The fourth and fifth rotation spots are open, and Leyland called the bullpen a "concern" because Bobby Seay (biceps) and Zach Miner (shoulder) may not be ready for opening day.
"Pitching, that's going to be the key every year and on every team," Leyland said. "That reminds me of a couple weeks ago when I said, `Some nights I go to bed thinking we have too much pitching and sometimes I wake up and don't think we have enough."
Leyland said right-hander Joel Zumaya, who threw in a simulated game on Thursday, needs to work on his breaking ball.
"We think that he's clearly doing something different and we will definitely make that adjustment," Leyland said. "He's not where I wanted him to be, but he did make some strides. The velocity is fine. We think he's going to be pretty good, but we've got some work to do with him."
Zumaya had right shoulder surgery last August.
Yankees owner George Steinbrenner attended the game. The Boss has been a regular at home games. ... Rodriguez had nothing new to report regarding his pending interview with federal investigators who are conducting a probe into a Canadian doctor accused of selling an unapproved drug. ... New York closer Mariano Rivera struck out one during a perfect seventh in his second appearance. He will pitch again on Sunday. ... Yankees LHP Damaso Marte, hit in the right lower back by a liner off the bat of Philadelphia's Ryan Howard Wednesday, is feeling "much better" and is scheduled to pitch Sunday. ... The Tigers also had a Friday night split-squad game against Atlanta. "We got action today. I like it," Leyland said.