Josh Hamilton contributed a three-run triple during that decisive seven-run frame for the Rangers, who took two of three in the series and have won five of seven overall.
"It just means we took 2-out-of-3. I'm not putting any more credence to it than we won the series," said Rangers manager Ron Washington when asked if it was a harbinger of success to come. "We did a good job of pitching in the two games we won. All three games we swung the bats, put some runs on the board, just [Saturday] they put more than we did. But it's about pitching, and we came in for two games and pitched pretty good."
Matt Harrison (11-9) yielded two runs on seven hits in seven innings for the win.
John Lackey (12-11) was rocked in the setback for eight hits and six runs with three walks over five-plus frames.
Michael Young's leadoff single in the sixth was followed by Adrian Beltre's 2,000th career hit, and Murphy followed with a single to plate Young -- for a 3-0 Texas edge.
"It was just another hit. I didn't give a lot to it until reporters asked me this morning," Beltre, the former Red Sox third baseman said of his milestone. "I didn't remember I just needed one. It was nice to do it here, where I played last year but I didn't give it a lot of thought."
Murphy went to second on a wild pitch and Napoli walked, ending Lackey's outing. Felix Doubront entered with the bases loaded but Moreland singled to plate one run and pinch-hitter Esteban German followed with a walk to force in another.
Kinsler's sacrifice fly made it 6-0, Elvis Andrus walked to re-load the bases and Hamilton cleared the sacks with a triple to make it 9-0 for the visitors.
"They made him (Lackey) work real hard from the get-go, as they do. When he missed, he just missed," said Sox manager Terry Francona of his starter's troubles. "Then we get to the sixth, 16 pitches in, nobody out and run in, we go to Doubront to try and stop it right there and it unraveled. Almost identical what they did [Saturday] happened to us today."
Boston finally hit the scoreboard in the seventh on Scutaro's two-run single, then climbed within 9-4 in the eighth on an Ortiz RBI hit and Darnell McDonald sacrifice fly.
Napoli started the ninth with a homer off the high wall beyond the bleachers in dead center and Kinsler's two-out blast cleared the Green Monster completely to provide the final margin.
Texas got on the board in the second when Murphy tripled to center with one out and Napoli followed with a base hit.
In the third, the Rangers tacked on another run as Endy Chavez led off with a double and Kinsler tripled. Kinsler was doubled off first thanks to a liner from Andrus and Hamilton flied out to keep it a 2-0 game.
Texas won six of the 10 meetings in the season series...Harrison won for the first time since August 8, going 0-1 with three no-decisions since then...Lackey has lost three of his last four starts, giving up at least four runs in each of those outings...Red Sox outfielder Conor Jackson left the game in the fourth inning after injuring his hand suffered when unsuccessfully tracking down Kinsler's third-inning triple and crashing into the low padded wall in right-center.