Will Middlebrooks followed with a line drive to left that took a bad hop off the Monster where the AL East standings are posted, and it got past Rodriguez 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.
"That Myers play obviously gave us some momentum," Victorino said. "All those kind of things and it became a snowball effect. Plays like that happen. You've got to thrive and you've got to get as many runs as you can when a mistake like that is made."
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 in the AL East. Every Boston starter got a hit and scored a run, the first time a team had done that in the postseason since Lou Gehrig, Joe DiMaggio and the Yankees in the 1936 World Series.
"No longer it's the best team, it's the hottest team," Gomes said. "And we obviously know Tampa is coming in hot, coming in on a roll. So it took a couple of innings to break the ice, but once Petey got that hit up the middle, I think that took a lot of questions out."
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!"
"Maybe our place in this market, this city, is we take those things to heart," Red Sox manager John Farrell said. "And in some ways this game and what we do here at Fenway is a vehicle to acknowledge others."
NOTES: Rodriguez made a diving catch of Gomes' sinking liner in the second inning. ... Lester went nine straight outings without allowing a homer before giving one up to Baltimore's Brian Roberts in his last start of the regular season. ... John Lackey will face David Price in Game 2, which is scheduled to start at 5:07 p.m. EDT on Saturday. ... Moore had been 10-1 in 16 road starts this season. ... The Rays used potential Game 4 starter Chris Archer to get four outs. ... Actor John Travolta was in the crowd.