Boston won the opener on Monday 2-0 in 12 innings, handing the Baltimore its fifth straight loss. The Red Sox improved to 6-1 against the Orioles this season as Brock Holt and Jackie Bradley Jr. lifted sacrifice flies against Mychal Givens.
The Red Sox received a further boost this series when right fielder Mookie Betts was back in the lineup Monday for the first time since May 26 from a left abdominal strain. He went 1-for-5 and is batting .354.
"He's good physically; mentally, no hesitation," Boston manager Alex Cora said. "The last few days have been great."
The Orioles (19-46) have the worst record in the majors and are the only team without at least 20 wins. The team must decide whether to completely rebuild over the coming weeks.
Rodriguez (7-1, 3.68 ERA) has been one of Boston's most dominant pitchers and will pitch the second game of the series. He has four of his last six starts with a 2.14 ERA. In his last outing June 6 against Detroit, Rodriguez allowed one run and five hits with five strikeouts and one walk over 5 2/3 innings. He lamented not pitching into the latter part of the game.
Rodriguez is 5-5 with a 3.97 ERA in 12 starts against the Orioles, who originally signed him as an international free agent in January 2010 and traded him to the Red Sox at the non-waiver trade deadline four years later for Andrew Miller.
"I've been feeling good. I've been trying to do the best I can," Rodriguez said. "My mentality right now is just thinking about to get more deep into games. Because as a starter you want to get more deep into a game than just 5 2/3 all the time."
The Orioles will counter with rookie David Hess, who has been one of the team's few bright spots this season. Hess (2-2, 3.07 ERA) took a hard-luck loss in his previous outing against the Blue Jays when he allowed just one run and five hits with four strikeouts and two walks over six innings on Thursday.
Hess took the loss in his only career appearance against Boston on May 20. He was charged with five runs and eight hits over just 4 2/3 innings but has performed much better since that game.
"I think that the confidence is definitely growing," Hess said. "I think that with every start, I get a little bit smarter, I guess, about what I need to do to have success and how to go about my business on an everyday basis. So, yeah, I think there's definitely progression with that and I'm excited that progression has come to where it is right now."
Baltimore shortstop Manny Machado was held out of the lineup in the opener because of an illness. His status for Tuesday is uncertain.
Struggling first baseman Chris Davis was back in the lineup for the second straight game Monday and went 0-for-5. He is batting just .150 on the season.