The Boston right-hander joins Carlos Zambrano of the Cubs, the Indians' C.C. Sabathia and the Angels' John Lackey as the Major's only 14-game winners.
Beckett was given a lead before he walked to the mound, as Boston's offense scored a pair of runs in the top of the first inning off Seattle starter Miguel Batista. Coco Crisp hit the game's third pitch into the right-field corner for a double and then scored on Manny Ramirez's sacrifice fly. Jason Varitek followed with a bases-loaded walk to give Boston a 2-0 advantage.
"I thought his stuff was real good," manager Terry Francona said following the victory. "He didn't always throw his breaking ball for strikes, but when [the batters] had to look for two pitches, he became very dominant."
Two runs would be enough for Beckett. He looked sharp early, tallying seven strikeouts over the first three frames and finished the game with nine punchouts in 6 2/3 innings of work.
The only damage off Beckett was a single in the sixth inning off the bat of catcher Jamie Burke that scored Ben Broussard with the Mariners' first run. A Yuniesky Betancourt groundout to shortstop Julio Lugo ended the Seattle threat, stranding two runners.
While Beckett's results were solid, his battery-mate said that Beckett was even better in his last two appearances.
"He was OK," catcher Jason Varitek said. "In his last two outings, he's gotten two losses and he was probably a little better. [He] pitched out of a couple of jams where he pitched real well, but he was a little off for me, wasn't as crisp, but still good enough. In the right situations, he made some really good pitches."
Beckett agreed that although he had good stuff, he struggled at times with his mechanics.
"I battled myself as far as being consistent with everything," the right-hander said. "Mechanically, not every pitch was the same."
Ramirez added a solo home run in the fifth inning, his 19th on the season. The two RBIs upped his career total to 1,588, which is 32nd on the all-time list, three behind Andre Dawson. Ramirez is also moving up the Red Sox's all-time RBI list. The left fielder is four away from matching Hall of Fame first baseman Jimmie Foxx for sixth on the club's RBI list with 788.
Boston won its fifth straight series by taking two-of-three from Seattle, and the Red Sox remain seven games ahead of the second-place Yankees.
"We don't have to sweep," Kevin Youkilis said. "I know a lot of times in Boston, everyone wants to win every game, but the main goal is to win every series any way you can. That's our goal each and every series."
J.D. Drew gave Beckett some more breathing room with a two-out RBI triple in the top of the seventh. Mike Lowell followed with an infield single that scored Drew and increased the Red Sox's lead to 5-1.
With the victory, Beckett improved his road mark to 7-1 with a 1.59 ERA in eight starts.
Chris Hester is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.