Stewart finished with two hits and Brett Gardner went 4-for-5 with a run- scoring single in the victory, the sixth in seven contests for the Yankees and third in this just-completed four-game series.
David Robertson (4-1) received the win after working a scoreless bottom of the eighth, with Mariano Rivera protecting the one-run lead in the ninth to earn the save in the retiring closer's final scheduled appearance in Seattle.
David Phelps held the Mariners to one run and three hits while striking out six over six innings while engaged in a pitchers duel with Seattle ace Felix Hernandez, who yielded a run on five hits and fanned seven through the first seven frames.
Yoervis Medina (1-2) took the loss after surrendering the go-ahead hit and run in the ninth.
"We can't keep watching this, we have to be better offensively," Mariners manager Eric Wedge said. "When we do create opportunities, we're not taking advantage of it. Having said that, we've got to create more opportunities. You're not going to come through every day, but we sure ought to do better than what we do right now."
Brendan Ryan's RBI single in the second inning was one of only six Seattle hits as the Mariners fell for the fourth time in five games.
After Robertson kept it a 1-1 game despite giving up a leadoff double to Alex Liddi in the bottom of the eighth. Ichiro Suzuki worked a walk against Medina to start the ninth and was pushed to second on Jayson Nix's sacrifice. Medina retired Reid Brignac on a fly ball for the second out, but Stewart was able to shoot a grounder through the left side and Suzuki easily slid in past a throw from Raul Ibanez in left.
"I do, I think he's going to score, because there's two outs, and he doesn't have to worry about not getting a good jump," Yankees manager Joe Girardi said. "Anything that's hit, he should be moving. You assume that he's going to score."
Rivera allowed a pair of singles, including one to Kyle Seager to begin the bottom of the ninth before he was erased on a double play, but managed to nail down his 23rd save of the season to tie Pittsburgh's Jason Grilli for tops in the majors.
Hernandez was able to work his way out of bases-loaded jam during an opening inning in which he walked a pair of Yankees, but was touched for a run as New York gained the early upper hand in the top of the second.
Nix began the frame with a single and stole second before crossing the plate on Gardner's one-out liner up the middle.
Seattle countered in its half of the second. Kelly Shoppach scorched a one-out double and advanced on a ground ball in front of Phelps' walk to Liddi. Ryan then hit a hard grounder in the hole that Nix got to with a diving attempt, but the shortstop's throw to second was late as Shoppach trotted home.
Phelps didn't give up a hit the rest of the day, issuing a third-inning walk to Seager before setting down 10 consecutive Mariners before being replaced by Boone Logan to start the bottom of the seventh.
Hernandez was equally as good, with the Yankees managing only two baserunners over the former Cy Young Award winner's final five innings. Gardner doubled and was stranded in the fifth, with Vernon Wells reaching on a Ryan error in the sixth.
The Mariners had an opportunity to move ahead when Liddi slashed an opposite- field double to open the last of the eighth and advanced to third on a Ryan bunt. Robertson came through with a big strikeout of Jason Bay, however, before fanning Nick Franklin as well to end the threat.
Seager's single in the ninth extended his hitting streak to 13 games ... Phelps has now not allowed a stolen base while on the mound in 103 consecutive innings, a streak dating back to August 18 of last season ... Gardner has gone 13-for-25 (.520) during a seven-game hit streak that has raised his season average from .256 to .284 ... New York had been 7-14 when failing to homer in a game before Sunday's result ... The Yankees improved to 8-3 in their last 11 visits to Safeco Field.
06/09 21:40:23 ET