Reliever Brandon League gave up a double to pinch-hitter Ryan Kalish and a single to Dustin Pedroia to put runners on first and third with one out in the 10th. Lefty Lucas Luetge then got Ortiz on a deep fly to right, but Kalish tagged and easily scored the go-ahead run.
The Mariners sit at 34-47 at the season's halfway point as Wedge continues searching for offensive answers, particularly at home where they've totaled nine runs in the first seven games of this homestand.
Though the Mariners tallied just four hits Sunday, they had numerous chances to score thanks to seven walks, a hit batter and three stolen bases. Yet they still crossed home plate just once in 10 innings after going 1-for-7 with runners in scoring position and stranding eight.
Vargas gave up just one run -- a solo home run by Pedroia in the eighth --- and five hits in an eight-inning performance. But the lefty wound up with a no-decision, leaving him 7-7 with a 4.31 ERA.
The long ball has bitten Vargas before this season, and he's now allowed a Major League-leading 22, the same number he gave up all of last year. But the one rip by Pedroia, a 388-foot shot down the left-field line on a 1-0 fastball, was the only blip on Vargas' radar the entire afternoon.
"It was just one pitch. I was pretty good the rest of the day," said Vargas. "He's a good player. He's shown he can put his team back in the game when he needs to. I wouldn't take it back. It was a fastball away. For him to hook it out of this park, you tip your hat to him and go on."
The Red Sox were just happy to tuck this one away in the win column and avoid a series loss after their potent offense was held to just nine runs in the series.
"You play four games here, guys get to thinking they're never going to hit one over the fence," said Red Sox manager Bobby Valentine. "Their pitching today was very good. Vargas had a terrific changeup and their bullpen was coming right after us with good stuff. I'm glad we were able to score two runs and get out of here with a split."
The Mariners had their shot in the bottom of the ninth again when Justin Smoak snapped a 1-for-29 slump with a one-out double off Vicente Padilla. After Dustin Ackley flew out, Chone Figgins walked, but Brendan Ryan flew out to right to end the rally.
After winning Saturday's game with a sacrifice fly in the 11th, Figgins wound up scoring Seattle's lone run in the third inning as he led off with a single to center, stole second, went to third on Ryan's base hit and scored on an Ichiro Suzuki sacrifice fly.
Seattle wasted a golden opportunity to add on in the fourth when Miguel Olivo and Smoak led off with walks. But Ackley was unable to get a sacrifice bunt down and wound up taking strike three, Olivo got caught in a rundown after thinking a pitch had gotten away from catcher Kelly Shoppach and Figgins grounded out.
"That was what cost us," Ackley said. "I had the perfect opportunity in that one inning to move the runners to second and third and I didn't get it done. If we take the lead there, they don't have a chance to go ahead there at the end. Those are the crucial times in a game."
It got worse for the Mariners in the fifth when they loaded the bases with one out, but Boston starter Felix Doubront was replaced by Matt Albers and the right-hander got Jesus Montero to ground into a double play on his first pitch.
Despite allowing just three hits, Doubront lasted only 4 1/3 innings thanks to five walks and a hit batter as the Mariners ran his pitch count up to 103 in a hurry.
Doubront had the highest run support in the Majors coming into the game at 8.44 per nine innings pitched, but the 24-year-old lefty didn't get much of that in his first Safeco appearance as the Red Sox couldn't get to Vargas until the eighth.
Vargas escaped a bases-loaded situation in the second when Kyle Seager made a diving catch at third of a line drive to his left by Nick Punto. Seager made another excellent stop in the fifth when he robbed Shoppach on a leadoff line drive with a leaping stretch, again to his left.
"It was good," Vargas said of his outing. "I attacked the strike zone, got them to put the ball in play early. There were a couple times where I had to make some pitches and was able to, and Seager made some great plays out there and kept the game where it was at. He did a heck of a job over there."