BOSTON — If knocking around the worst team in the American League is your idea of a good time, it’s a lot of fun to be a Red Sox fan right now.

Thank goodness for the Tampa Bay Devil Rays. Tucked in the bottom of the A.L. East, the hapless Rays look to be frequent fodder for the Sox this summer. The Sox clubbed the Rays last night at Fenway Park, 15-4, to complete a three-game sweep and push the record of potential All-Star Game starter Josh Beckett to a sterling 12-2.

This could be just the start for the team with the best record (53-31) in baseball. The Sox and Rays are set to meet 15 more times over the final 78 games of the season, or a shade less than 20 percent of the year’s remaining games. That may be the best reason yet for Boston fans to sleep well and dream of big October games.

“That’s a lot of runs,” said Beckett, who’s seen his teammates score nearly eight runs a game in his 16 starts. “These guys never cease to amaze me with the way they swing the bats.”

Tampa, now 33-51 and 20 games behind Boston in the standings, was at its worst last night. Devil Rays’ starter J.P. Howell, the same J.P. Howell who’s already logged two starts against the Pawtucket Red Sox this season, suffered through the embarrassment of not surviving the first inning. The Sox batted around and scored six times in the opening frame, chasing Howell (1-3) before some fans had even found their seats.

The rest of the Devil Rays’ pitchers weren’t a whole lot better. The Red Sox scored three more times in the second inning and four times in the third to race to a 13-2 lead. That led to a few hours of meaningless mop-up ball where both managers liberally emptied their benches. Boston knocked out season-highs in both runs and hits (21) against seven Tampa pitchers.

Coco Crisp cracked the second grand slam of his career in the first inning. Mike Lowell hit a 3-run smash in the second, racked up five RBI and set a career-high with five hits. The struggling David Ortiz snapped a 4-for-28 skid with three hits.

“It was a good way to play a game, nice to get an early lead and spread it out,” said Boston manager Terry Francona. “We got into their pen early and put them in a difficult position.”

Beckett is used to getting big run support but nothing like last night. The Red Sox have scored an average of 7.69 runs in his starts before last night. Staked to a massive lead, Beckett had little trouble bouncing back from the shaky performance in his last outing against Texas. He cruised through six innings, allowing three runs on nine hits. He struck out nine hitters and isn’t scheduled to pitch again for the Sox for more than a week. He is headed to the All-Star Game, however, and may be the A.L.’s starting pitcher.

“It’s exciting,” he said of the chance to start in his All-Star debut. “It’s completely out of my control but it’s exciting. I’ll be happy if he (Detroit manager Jim Leyland) chooses me.”

The first three innings were straight out of a Sunday morning beer league and the Red Sox owned all of the best thumpers. In the first, Manny Ramirez singled in J.D. Drew for the game’s first run but Howell walked Jason Varitek with the bases loaded to walk in a second run. Crisp then crushed a pitch off the Coke bottles high above The Wall in left field to make it 6-0.

Reliever Brian Stokes retired Dustin Pedroia, the 11th batter of the first inning, on a flyout to end the frame but he wasn’t as lucky in the second. Ortiz led off with a double, Ramirez walked and Lowell cracked his team-leading 14th homer down the left-field line to make the score 9-0.

Jon Switzer came on for the third inning but Boston’s bats kept booming. An Ortiz single, a double by Ramirez and RBI single by Lowell made it 10-0. Varitek reached on an infield hit and a walk to Crisp loaded the bases. Julio Lugo then lined a two-run single into center to push the lead out to 13-2.

From that point on, the game quieted down a bit. Beckett gave up two runs in the top of the third when he allowed two doubles and a walk. He put two runners on base in the fourth and fifth but avoided any further damage. In the sixth, the Rays scratched out a Delmon Young double, a sacrifice fly and an infield hit by Dioner Navarro. Beckett left with a 13-3 lead after throwing 105 pitches.

Kyle Snyder allowed a single run in the seventh but Mike Timlin came on and pitched two shutout innings to mercifully end the 3-hour, 36-minute mismatch that ended in a downpour.

kmcnamar@projo.com