With a sellout crowd at Tropicana Field on its feet, James Shields struck out Rodriguez looking on a 3-2 pitch. After the out, Rodriguez briefly discussed the call with plate umpire Bill Welke before heading to third base to play defense.
Yankees manager Joe Girardi decided to partially rest A-Rod on Sunday, and plans to give other regulars a break in the near future.
"He's played 13 days in a row," Girardi said. "We've got to make sure that we keep him healthy and strong. My key is keeping our guys healthy the rest of the way. It could be a very tough two months. If you don't do that, shame on us."
The Yankees' third baseman went 0 for 3 with a walk, a strikeout and a run scored Saturday in a 5-4 win. It was his ninth game since hitting his 599th homer on July 22.
"My swing is a little out of whack," Rodriguez said.
Rodriguez said he really didn't need a day off, but understands Girardi's desire to keep his players fresh. He is hitting .237 (9 for 38) with eight RBIs since getting within one homer of 600.
His next opportunity for No. 600 could be at Yankee Stadium on Monday night against Toronto.
"It will come," Rodriguez said. "Everything is going to be fine."
The Yankees have the best record in baseball.
"That's been the good part, we've been winning," Rodriguez said. "The team has been playing well and we've been getting picked up by different guys."
Girardi said it was a tough decision to rest Rodriguez against the Rays, who are second in the AL East.
"But it's not September 25th," Girardi said. "If I run him out there and he gets hurts today, people are going to say, why did you play him 13, 14 days in a row? You've got to be smart about it."
Also, left-hander Andy Pettitte (strained left groin) threw 25 pitches halfway up a bullpen mound and could have a full mound session Tuesday or Wednesday.
"Everything is going good," Pettitte said. "It's another step."