Justin Masterson (4-10), facing his old club for the first time since he was dealt at the trade deadline last season, earned the win by scattering four hits and a run despite walking four over five-plus innings.
"We knew we had a tough pitcher in front of us, and all we asked the team to do was get quality at-bats and run up his pitch count and we did," Indians manager Manny Acta said. "We kept putting pressure on. Every day it is tough against these guys because we have faced three top-of-the-rotation type of arms. We have to give credit to our guys because they really battled hard and we scored enough runs."
Jon Lester (11-7) yielded seven hits and four runs -- two earned -- over five- plus frames in defeat.
Already ahead 4-1, the Tribe locked up the game with an offensive barrage in the seventh.
Jason Donald singled and Asdrubal Cabrera reached on a fielding error ahead of an intentional walk to Shin-Soo Choo. Shelley Duncan grounded into a fielder's choice to score a run, two batters later Nix lofted a sacrifice fly to center to plate Choo, and Marte capped the run by hitting a three-run blast to left for a 9-1 game.
Cleveland hit the scoreboard in the third as Marte walked. Trevor Crowe singled, then Marte scored when Lester threw wild to third on Lou Marson's grounder.
Cabrera's sac fly and a Duncan RBI double pushed the visitors' edge to 3-0 in the fifth, then Nix led off the sixth with a homer.
Ortiz followed suit for the Sox in the home sixth but Boston was unable to muster any more runs.
"I mean, he's tough," Red Sox catcher Kevin Cash said of Masterson. "He's got a good sinker and a good slider, and tonight he had his four-seamer going, too. He went to that, it seemed like a lot. He had both sides of the plate with his fastball. When he's got that kind of movement, you're going to see a lot of ground balls and a lot of swing and misses, which he got tonight."
Coming into the game, Masterson was 8-2 with a 3.61 ERA in 36 games at Fenway Park...The Indians have won four of seven from the Red Sox this season...Adrian Beltre was the lone Red Sox starter to have more than one hit...Donald finished 2-for-5 and scored twice, while Choo walked twice.