The Rays try to prevent the visiting Yankees from matching a season high with their sixth consecutive victory Friday night.
Though Rodriguez won't answer any non-baseball related questions, each city New York (68-59) visits of late naturally brings with it the distraction surrounding the embattled third baseman.
Tampa Bay manager Joe Maddon won't feed the fire or tell his pitchers to intentionally throw at Rodriguez like Boston's Ryan Dempster did Sunday.
"Vigilante justice and unilateral decisions, I'm not into that stuff," Maddon told the Rays' official website. "That is totally separate from the unwritten rules of baseball."
Especially considering the Yankees have averaged 5.4 runs and hit 21 homers while batting .290 in 17 games since Rodriguez made his 2013 debut. Curtis Granderson homered and Andy Pettitte threw six strong innings Thursday as New York won for the 11th time in 14 games, 5-3 to sweep four from Toronto.
"We're feeling good about ourselves, and you knew this was going to happen," Pettitte said. "It was just a matter of when, and you hope it's not too late."
The Yankees are 3 1/2 games out of the final wild-card spot in the AL. The Rays (72-53) lead that race and trail first-place Boston by a game in the East. Tampa Bay leads 7-6 in the season series with New York, with each team winning three times at Tropicana Field.
Tampa Bay has won six of eight overall and 18 of 23 at home, but it faces a stiff challenge against New York starter Hiroki Kuroda (11-8, 2.41 ERA).
The right-hander has the lowest ERA in the AL, but he allowed five runs - three earned - and a career-high 11 hits in 5 2-3 innings of a 6-1 loss at Boston on Saturday. The five runs matched the total he yielded while going 4-1 in his previous seven starts.
Kuroda went 2-1 against the Rays last season despite posting a 6.11 ERA.
New York hopes the streaky Alfonso Soriano can break out of his 1-for-19 slump that followed a five-game stretch where he went 15 for 22 with five homers and 18 RBIs.
The Yankees also must try to solve Rays starter Chris Archer (6-5, 2.95), who has given up one run in 15 innings to win both 2013 starts against them. He tossed a two-hitter and won 1-0 in the Bronx on July 27.
"Regardless of the venue or team, I'm trying to go out there and accomplish the same goal every day: Be mindful of every pitch (and keep) my team in the game as long as I possibly can," the right-hander said.
Since that dominant performance, Archer is 0-2 with a 4.79 ERA in four starts. He yielded a run and four hits in seven innings of a 2-1, 10-inning win over Toronto on Sunday.
Tampa Bay rookie Wil Myers is 11 for 31 (.355) with three homers and nine RBIs in seven games against New York this season.
Looking to perhaps boast their roster for the stretch drive, the Rays signed veteran Delmon Young to a minor league deal Thursday. Released by Philadelphia last week, the former No. 1 overall pick of the Rays hit .293 with 16 homers and 103 RBIs in 192 games for them in 2006-07.