The Red Sox loaded the bases in the bottom of the eighth with two outs, but Shingo Takatsu struck out pinch-hitter Jason Varitek.
Takatsu issued a one-out walk to Ortiz in the ninth and Millar followed with a two-run homer before Takatsu got the last two outs for his 11th save in 12 chances.
Yankees 11, Mariners 3
In Seattle, Ruben Sierra hit a grand slam and drove in five runs, and Jon Lieber pitched eight strong innings. Bernie Williams added a three-run homer and Jorge Posada hit a solo shot for the Yankees, who lead the majors with 178 homers.
Despite playing without All-Star third baseman Alex Rodriguez, who missed his first game of the season with the flu, the Yankees routed the last-place Mariners and improved to a season-high 33 games over .500 at 74-41.
Lieber (9-7) won his second straight start. He gave up three runs and seven hits, struck out four and walked none.
Ron Villone (4-3), making his seventh start of the season, gave up eight runs on 10 hits.
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