Rodriguez has come out of the All-Star break strong, winning both of his starts while giving up three runs in 13 1/3 innings. Last time out, he allowed two runs on three hits in 6 1/3 innings against the Blue Jays.
"I mean, for me, just right now going up there and get innings, that's my goal," Rodriguez told the Boston Herald. "Get up there and get as deep as I can in the game."
Rodriguez is 0-2 with a 7.11 ERA in four starts at Tropicana Field.
Tampa Bay's Travis d'Arnaud smacked his first career grand slam and Blake Snell pitched six shutout innings in Sunday's win.
"That was a tough five games, and that's why this win was so big, to give us that momentum to go into one of our division rivals in the Red Sox," d'Arnaud told MLB.com. "It'll be a good series, and hopefully we can be up 1-0 after tomorrow."
The struggling Rays offense managed just three hits and was unable to add runs after d'Arnaud's homer, but Snell and three relievers made the lead stand.
Emilio Pagan, who gave up a game-tying homer in the ninth inning of Saturday's loss, struck out the side in the eighth.
"Definitely more so for the psyche of the team," Pagan told the Tampa Bay Times regarding the importance of closing out Sunday's win on the eve the series against Boston. "It was huge to be able to hold on to that lead there and finish it off."
Tampa Bay also got good news off the field. Center fielder Kevin Kiermaier sprained his left thumb sliding into first base Saturday but will not need surgery and should miss only 10-15 days.
Beeks, who will likely serve as the opener on Monday, last worked on July 16 against the Yankees when he gave up a run on two hits in 3 1/3 innings of work.
He is 2-0 with a 2.89 ERA in two appearances against the Red Sox.
Boston saw its streak of 81 games without being shut out end in Sunday's 5-0 loss. It was also the first time in 11 games the Red Sox failed to hit a home run.
The Red Sox are 5-5 since the All-Star break, and now the defending champions have 14 straight games against the New York Yankees and the Rays.
"It's just tough," Boston's Mookie Betts told the Herald. "Tough situation we're in. Every game is important. It's just one of those things where we just have to turn the page and get ready for (Monday)."
--Field Level Media