Jed Lowrie homered twice for Boston, which is seven games behind New York and third in the AL East.
League (9-7) entered the game in relief of starter Luke French and quickly retired his first two batters. Victor Martinez and Adrian Beltre followed with a pair of singles and League served up a fastball on the inner half of the plate that Ortiz drilled over the wall in right-center field to give the Red Sox a 7-5 lead.
The Mariners added a run in the ninth inning. Rich Hill (1-0) got the win in his first appearance since July 27, 2009 with Baltimore.
After League walked Varitek to lead off the ninth, Eric Patterson stole second as a pinch runner, moved to third on a groundout by Daniel Nava and scored on a fielder's choice by Ryan Kalish. Josh Reddick followed with an RBI single to make it 9-5.
Lowrie hit his first of two home runs off French in the second inning with a runner on to put the Red Sox on top.
Lowrie struck again in the fourth with a solo shot over a leaping Michael Saunders to take a 4-2 lead. French managed to settle down and retire his final 12 batters.
Daisuke Matsuzaka drilled Josh Wilson to lead off the fifth inning and Seattle capitalized on the mistake. Ichiro Suzuki doubled to left-center field to score Wilson from first. After Chone Figgins reached on a bunt, Russell Branyan hit a sacrifice fly to right field to score Suzuki and tie the game at 4.
A leadoff single from Suzuki chased Matsuzaka in the seventh inning. Figgins sacrificed Suzuki to second base and Gutierrez drove him in with a two-out double off the wall in left-center field to give the Mariners the lead.
Notes
Red Sox C Jason Varitek got his first start since June 30 against Tampa Bay. Varitek missed two months with a fracture in his right foot. He was 0-for-3 with a walk. … The Mariners ran on Varitek six times, stealing four bases. … 3B Adrian Beltre set a Red Sox record with his 71st extra-base hit of the season, a double in the second inning, moving out of a tie with Wade Boggs. The double also moved him into the lead for most extra base hits in the majors this season, surpassing Evan Longoria of Tampa Bay. … Figgins' four hits were a season high.