Cleveland manager Mike Hargrove recorded his 700th victory as the Indians won their third straight in the series. At 76-47, the Indians have the best record in baseball and are a season-high 29 games over .500.
Mesa (1-5), who gave up a run to the Indians in the ninth to tie the score for his fourth blown save, walked Manny Ramirez with one out before Sexson hit a 1-1 pitch 381 feet over the right field fence.
David Riske (1-0) struck out three in 1 2-3 innings to get his first major league victory in his fifth appearance for the Indians.
Mike Jackson pitched the 10th for his 29th save and second of the series.
Mariners manager Lou Piniella was ejected after a heated argument with second-base umpire Bill Welke after Carlos Baerga stole second base. It was Piniella's third ejection of the season. It appeared on TV replays that Baerga went out of the base line to avoid shortstop Alex Rodriguez's tag.
When Piniella came out of the dugout he stumbled and fell as Hargrove watched and laughed.
Griffey's AL-leading 38th homer came after Paul Shuey struck out pinch-hitter Tom Lampkin, but Lampkin reached first on a wild pitch. Griffey, who also tripled and had four RBIs, then hit a 1-1 pitch off Assenmacher, who suffered his second blown save of the season.
Ramirez put the Indians ahead 3-2 by leading off the sixth with a homer, his 33rd, off starter Jamie Moyer.
Chris Haney, released at the end of spring training by the Los Angeles Dodgers, made his first start of the season for the Indians.
Haney, 30, was called up from Triple-A Buffalo on July 22 and appeared in five other games for Cleveland. In six innings, Haney gave up two runs on five hits and two walks, while striking out six.
Moyer went 7 1-3 innings, allowing three runs on eight hits and one walk.
Cleveland went ahead 1-0 on Enrique's Wilson RBI double in the third before Griffey's two-triple made it 2-1 Seattle in the bottom of the inning. The Indians tied the score at 2 when Einar Diaz led off the fifth with his third homer of the season.
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