Giambi, who went 2-for-5 with his 15th home run in the series opener, has a hit in four straight games.
With Giambi out, rookie Kevin Thompson made his Major League debut in right field and Bernie Williams was the designated hitter. Catcher Jorge Posada batted in the cleanup spot for the second time this season.
Rodriguez was not in the lineup again Saturday, and spent most of the time before the game in the trainer's room.
"He's better, but he's not there yet," said manager Joe Torre. "He had a little bit of a better look on his face today."
Torre said if Rodriguez stayed around for the whole game and dressed that he could be available to pinch-hit.
Closer Mariano Rivera said he was feeling better Saturday and expects to be ready to pitch again Monday, when the Red Sox visit Yankee Stadium.
"He's feeling better every day," Torre said. "He's doing his exercises and taking his treatment."
Rasner placed on DL:
Reliever Darrell Rasner felt discomfort in his right shoulder while warming up in the bullpen Friday night, and was put on the 15-day disabled list before Saturday's game.
"In all probability, it will be gone in a few days," Torre said. "It's nothing major, but where we are at this point in time, with Mariano down for a couple of days, we just can't afford not to have an arm here."
Lefty Matt Smith was recalled from Triple-A Columbus for the third time this season, and was expected to arrive in Baltimore around 7 p.m. ET.
New York's bullpen was short again Saturday with Rivera out and Kyle Farnsworth unavailable because of his extended work in each of the past two games. Farnsworth threw 29 pitches Thursday in Detroit, and went 1 1/3 innings Friday, picking up the win.
Torre said before the game that the team would likely use Scott Proctor as its closer Saturday.
Melky Cabrera, who's batting .315 with a five-game hit streak, showed off another one of his skills Friday night.
With two runners on and two outs in the second inning, Brian Roberts singled to left. Cabrera fielded the ball cleanly and fired a strike to catcher Kelly Stinnett, who tagged out Javy Lopez to end the inning.
"It was pretty impressive," Torre said. "Not only the arm, but the accuracy of the arm is probably the most impressive thing."
New York wraps up its seven-game road trip Sunday, starting Aaron Small (0-2, 7.78). Righty Rodrigo Lopez (3-7, 6.88) will pitch for Baltimore.