BOSTON  Maybe it really was just the American League East’s bad dream.

Maybe last season’s surreal ascent of the Tampa Bay Rays from laughingstock to division champions  culminating in the Rays beating the Red Sox for a berth in the World Series  was, indeed, too bizarre to have actually occurred. On Tuesday, the cosmos did seem realigned at Fenway Park, where the Red Sox dismissed the Rays, 5-3, to land the first solid jab in the division.

The Boston ace Josh Beckett struck out 10 through seven breezy innings in his first opening-day start for the Red Sox. His bullpen gave up two runs in the eighth to narrow the score, but Beckett was as dominant as the Red Sox expect him, and themselves, to be all season.

“We’ve got a long way to go, but watching the way he’s throwing is big,” Manager Terry Francona said of Beckett, whose command of his fastball and curveball were in virtually midseason form. “We want to lean on him.”

Tampa Bay struck out 14 total times  Carlos Peña in each of four at-bats  and managed only three hits. The Red Sox’ lineup proved as balanced as the Rays’ was feeble, with Dustin Pedroia (first inning) and Jason Varitek (fifth) hitting solo home runs, and Jason Bay and Mike Lowell each adding run-scoring hits in a three-run third. All the runs came off James Shields, who appeared simply overmatched despite his talent.