The lefty would get two outs in the inning, but couldn't escape after putting two men on via walks to Avisail Garcia and Christian Arroyo. "We'll say the wind had some carry on it".
Rays first baseman Brandon Lowe had a big day, hitting two home runs and driving in three. Guillermo Heredia and Yandy Diaz also hit solo shots for the Rays. Whether that is a good or bad sign is subject to speculation, but this latest development is certainly frustrating for the Red Sox, who invested heavily in Eovaldi, rewarding his late-season heroics with a four-year, $68MM contract last winter.More news: Spielberg's latest horror can only be watched at night
"They're a good team", Boston manager Alex Cora said. "I've been saying it all along, it's a complete team".
Reigning American League Cy Young award-winner Blake Snell stymied Red Sox hitters over six innings of work, allowing one run on five hits. Travis d'Arnaud slapped a one-out sacrifice fly to right field to score Lowe for Tampa Bay's second run of the afternoon.
Rodriguez (6-4) gave up four runs and seven hits in 5 2/3 innings with seven strikeouts.More news: Mexico denies Trump's claim of secret concessions in deal
Boston got the first two runners on in the opening two innings but scored just a run on Marco Hernandez's RBI single in the second. They broke into "Let's Go Bruins!" cheers later.
Tampa Bay reached 40 wins in its initial 64 games for only the second time in its history after doing it in 62 games in 2010. David Price earned his fourth victory and Michael Chavis went 1-for-3 with a double and two RBIs for Boston.
Red Sox Injuries: Hector Velazquez: 10-day IL (back), Tyler Thornburg: 10-day IL (hip), Brian Johnson: 10-day IL (elbow), Nathan Eovaldi: 10-day IL (elbow), Dustin Pedroia: 60-day IL (knee), Steve Pearce: 10-day IL (back), Mitch Moreland: 10-day IL (quad), Tzu-Wei Lin: 10-day IL (knee), J.D. Martinez: day-to-day (back).More news: TV licence fees for over-75s will be means-tested
Hernandez would undergo two more surgeries, with the third coming last July.