Each club has fallen short of expectations, has crowded its respective disabled list and trail the Yankees in the American League East.
The second half of the season will start for both teams Friday, when Boston visits Tropicana Field to take on Tampa Bay.
Jeremy Hellickson is slated to open up the series for the Rays, starting for the first time since July 5, when he took the hill for the first time since June 30, when he was hit on the right leg by a Prince Fielder line drive.
Hellickson, pitching against the Indians on July 5, allowed solo homers to leadoff hitter Shin-Soo Choo and then Michael Brantley in the first inning, but he improved, adding four scoreless innings and earning a quality start.
"Started off pretty rough," Hellickson said. "Once I started commanding my fastball, I started settling down."
Tampa Bay will be happy to be back at home after limping into the All-Star break as losers of nine of its last 14 games. Tropicana Field still hasn't been too friendly to the Rays, who are 24-19 at home this season.
Boston, meanwhile, may not mind hitting the road after the break, after finishing two games above .500 during the first half in away games. The Sox are 22-24 at Fenway Park after dropping Sunday's matchup with the Yankees.
"I would say that it was extremely challenging," Sox manager Bobby Valentine said of the first half. "I don't know how to rate it or anything, but Major League Baseball is very challenging. Managing a new team is very challenging, and we had some situations that added to the mix.
"But I'm very optimistic. The guys I have today, I think we can win a ballgame with. And the guys I have after the break I think will be the same type of group."
Franklin Morales will make his fifth start for the Red Sox. The left-hander struggled in his last outing, giving up four home runs in 3 1/3 innings against the Yankees on Saturday. In his first three starts, though, the former reliever struck out 24 in 18 innings and posted a 2.00 ERA.
The last time Morales faced the Rays, on May 27, he plunked Luke Scott in the top of the ninth inning and the benches cleared at Fenway Park.
Red Sox: Ellsbury to return
Center fielder Jacoby Ellsbury hasn't played for Boston since an April 14 game against Tampa Bay, but he was in the lineup when it was posted Friday.
Ellsbury batted .185 (5-for-27) with one homer and three RBIs in eight Minor League rehab games spread across three levels of the Red Sox's farm system.
The 28-year-old was hitting .192 with three RBIs in seven games for the Red Sox before partially dislocating his right shoulder injury while trying break up a double play.
Rays: Longoria likely out until August
Tampa Bay announced on Saturday that third baseman Evan Longoria will begin baseball activities after the All-Star Game and will presumably be out until August.
Longoria partially tore his left hamstring on April 30, and he was originally expected to be out six to eight weeks, but he has not made significant progress nearly 10 weeks later.
On June 18, Longoria attempted a rehab assignment with Triple-A Durham, but he left the game because of discomfort. In the 23 games before the injury, Longoria was hitting .329 with four homers and 19 RBIs.
The season series is a 4-4 split between the two clubs. Tampa Bay took two of three at Boston May 15-17.
Red Sox designated hitter David Ortiz has a team-best .312 average, with 22 home runs and 57 RBIs.