BOSTON >> One ball fell between two outfielders. Another took a bad hop off the Green Monster standings. One batter reached safely on a dropped third strike and another when the pitcher was slow to cover first.

By the time it was over, the Boston Red Sox had scored five runs in the fourth inning, taking advantage of Tampa Bay’s bad luck and bad defense to beat the Rays 12-2 today in Game 1 of the AL division series. 

Every Boston starter got a hit and scored a run. The Red Sox tweeted that it was the first time a team had done that in the postseason since 1936 — Lou Gehrig, Joe DiMaggio and the Yankees did it in the World Series.

Needing a 163rd game to earn a wild-card berth, the Rays took three win-or-go home matchups in three different cities to reach this series. Now they need a victory in Game 2 on Saturday to tie the series before the teams shift to St. Petersburg, Fla., for Games 3 and 4. 

Jon Lester allowed three hits in 7 2-3 innings for the AL East champions, giving up a pair of solo homers over the Monster by Sean Rodriguez and Ben Zobrist to spot the Rays a 2-0 lead through the top of the fourth. Tampa Bay starter Matt Moore had still not given up a hit.

But Dustin Pedroia led off the bottom half with a single up the middle, and then David Ortiz hit a high fly ball that center fielder Desmond Jennings and rookie right fielder Wil Myers converged on. Myers raised his left hand to call off Jennings but let it fall behind him, bouncing off the warning track a few feet in front of the fence and into the bullpen for a double.

With a derisive cheer of “Myers” echoing through the ballpark, Mike Napoli popped up to second base for the first out before Jonny Gomes hit a fly ball that scraped the left-field wall on the way down. Pedroia held to tag up, then scored easily with Ortiz coming in just a few steps behind him to make it 2-2.

Jarrod Saltalamacchia struck out before Stephen Drew hit a slow hopper to first that James Loney fielded and flicked to Moore. But the pitcher’s foot came down a split second after Drew’s and, with Moore facing the wrong way, Gomes never slowed down as he rounded third and scored without a throw.

Will Middlebrooks followed with a line drive to left that took a bad hop off the AL East standings and got past on the rebound. That allowed Drew to score and make it 4-2, while Middlebrooks went into second with a double. Jacoby Ellsbury reached on a passed ball on strike three — which would have been the third out of the inning — and Middlebrooks moved to third, where he scored on Shane Victorino’s single to make it 5-2.

None of the misplays was scored an error.

The Red Sox added three more runs to chase Moore in the fifth inning when they sent nine batters to the plate — the first time in franchise history they have batted around in consecutive innings in a postseason game. In all, Moore was charged with eight runs — seven earned — on eight hits, two walks a hit batter and a wild pitch, striking out four in 4 1-3 innings.

Lester struck out the first four batters he faced, but gave up solo homers to Rodriguez in the second and Zobrist in the fourth. In all, he allowed three hits and three walks while striking out seven before leaving with two on and two out in the eighth. 

Junichi Tazawa got Myers on a line drive to right to end the eighth, and extra starter Ryan Dempster got the last three outs. Victorino had three hits and Saltalamacchia had three RBIs for the Red Sox, who tied for the best record in baseball this season a year after finishing last.

The clubs got to the ballpark for the series opener to find the tarp on the field, but the rain let up a few hours before game time and made way for a pregame ceremony to honor the victims and first-responders of the Boston Marathon bombings. With a giant “B Strong” logo mowed into the center field grass, the families of the late Krystle Campbell and Sean Collier took the field, followed by marathon volunteers, doctors and nurses, police officers and others who helped out after the April 15 explosions that killed three and wounded at least 260 more.

Campbell was one of three people killed in the bombings. Collier was a MIT police officer shot during the manhunt for the bombers. 

Players, managers and coaches from both teams lined up on the first- and third-base lines and applauded throughout the ceremony. A giant U.S. flag was draped over the Green Monster for the national anthem, and Cowboy-hatted good Samaritan Carlos Arredondo joined former New England Patriot Joe Andruzzi to shout the traditional “Play Ball!”