Neither team has found much to get excited about at the start of this season, though.
Boston and Tampa Bay meet for the first time since their postseason encounter as they begin a three-game set Tuesday night at Fenway Park.
The Red Sox won their third title in 10 seasons in their first year under manager John Farrell, first getting past the Rays in four games in the division series.
Boston (12-14) has struggled at times in 2014, however, and has failed to win more than two straight. After scoring 15 runs while winning the first two games of its series with Toronto, it fell 7-1 on Sunday as Xander Bogaerts recorded two of the team's six hits.
The Red Sox now begin an eight-game stretch at home, where they're 5-8.
"How we play at Fenway Park is going to be pivotal for us," Farrell said.
Tampa Bay (11-15) sits one spot behind Boston in last place in the AL East and has lost five of six after falling 7-3 to the Chicago White Sox on Monday. Matt Joyce and David DeJesus each had an RBI for the Rays, who have dropped six of seven on the road.
They've also been hindered by multiple injuries to their starting rotation, as Matt Moore (Tommy John surgery) and Alex Cobb (oblique strain) remain out. Veteran Erik Bedard, who began the season in Triple-A, will take the mound for the series opener after struggling in his first two starts.
Bedard (0-1, 7.45 ERA) gave up four runs in 3 2-3 innings of an 11-5 win over the Yankees on April 18 before allowing four runs and walking five while throwing 90 pitches in four innings of Thursday's 9-7 loss to Minnesota.
The left-hander was called up from the minors April 12 to be a long reliever, but he was thrust into the rotation due to injuries.
"Hopefully next start I'll throw more strikes and get quicker outs," Bedard said.
The Red Sox acquired Bedard from Seattle in a three-team deal July 31, 2011, and he went 1-2 with a 4.03 ERA in eight starts. Bedard has faced Boston once since leaving as a free agent following that season, giving up five runs in three innings of a 7-3 loss while with Houston last April 26.
He's 2-4 with a 7.76 ERA in seven starts against the Red Sox at Fenway Park, and he'll look to improve on that mark as he opposes John Lackey (3-2, 4.22).
Lackey gave up six runs and 10 hits in each loss to the Yankees on April 12 and Baltimore on April 18, but he bounced back with his best start of the year Wednesday when he allowed one run and struck out 11 over eight innings of a 5-1 victory over New York.
''I was thinking about trying to give the bullpen a rest,'' Lackey said. ''We've got some guys down there who have been working pretty good. I just wanted to get those guys a little bit of breather and win a ballgame.''
The right-hander hasn't been able to do that in his last four starts against the Rays, going 1-2 with an 8.84 ERA while pitching fewer than six innings in each. Lackey gave up four runs and walked three in 5 1-3 innings of a 7-4 victory in Game 2 of last season's division series.