Francisco Cordero struck out Phillips swinging to end the eighth, and the Rangers made the two runs they'd scored in the top of the eighth hold up in a 4-2 win over the home team before a damp crowd of 41,115 at Yankee Stadium.
"Jeter took a great at-bat," Giambi said after the game. "It would have been nice if I'd been able to hit there, but I probably wouldn't have been able to do much. It was better to get out and not make it worse. Ice it, heat it and get it to relax."
Even the powerful Yankees can ill-afford to lose another bat. Right fielder Gary Sheffield is on the disabled list for at least another week with a wrist injury, and left fielder Hideki Matsui is out for three months -- and maybe the season -- with a wrist injury that required surgery last week.
"Certainly we lost two guys, but we can't go there," Yankees manager Joe Torre said of a team that has scored just three runs while losing two straight games.
Giambi said he hopes to be in the lineup against the Rangers on Tuesday night, but admitted he could miss a day. Torre said a doctor will examine the veteran slugger on Tuesday.
"When he came to me he just had trouble turning," Torre said. "He may have strained it when he drove for the ball."
Giambi strained his neck when he made a nice stop by diving headlong toward the line on a hard smash by Michael Young in the third inning. Giambi extended full length to make the stop, got up and his flip to pitcher Mike Mussina at the bag was late.
"I guess when the ball popped out I kind of jammed my shoulder turned my neck," said Giambi, turning the entire top half of his body as he answered a question asked by a reporter standing to his right.
The loss was a tough one for the Yankees, who had hoped to get back to winning with Mussina on the mound. At 6-1, the veteran right-hander had won five straight starts and the Yankees were facing Texas veteran right-hander Kevin Millwood, who was 0-3 lifetime against New York and coming off a start in which he gave up nine runs to the Twins in 1 1/3 innings on May 9.
The Yankees got to Millwood for single runs in the second and fourth innings, but that was it. Millwood improved to 4-3 by working seven innings to five-hit, six-strikeout, no-walk baseball and Mussina had to leave the with the score tied at 2 after seven innings because his pitch count had reached 105.
Kyle Farnsworth (1-1) took over for Mussina to start the eighth and promptly gave up a leadoff double to Gary Matthews Jr. that hugged the foul line as it rolled into left field. Matthews had to hold at second on a grounder to the mound, but took third on a wild pitch and scored on a single to right by Mark Teixeira.
Farnsworth walked Phil Nevin, and Hank Blalock lined a single to center to produce another run.
Second-year second baseman Robinson Cano had a big hand in both his team's runs.
Cano led off the second with a single, raced to third on a groundout to third one out later and scored on a single to right by Bubba Crosby. Alex Rodriguez lined a hard double to left-center to open the fourth and scored on a single by Cano.
But Texas tied the game in the fifth on a homer by Brad Wilkerson and two singles and a sacrifice fly.
"He's a good pitcher, but we had our chances," Yankees leadoff hitter Johnny Damon said after going 0-for-4 for a team that had one hit after the fourth inning. "We had a couple of balls to hit. If I'm not going it makes it a little tough for this offense to go. So I have to get a little more consistency.
"We're missing a lot of guys in the lineup, but we need to stay within the game plan. Hopefully that will work out for us. We're just swinging and missing a little bit and now is not the time to do it. We've got to pick up the slack until at least Sheffield gets back."