Chavez singled and scored in the first inning, then ended the night for Cleveland starter Trevor Bauer with a solo home run into the right-field seats with one out in the seventh. It was Chavez's first homer since May 30, 2013, at San Diego, a span of 265 plate appearances.
Kyle Seager had two hits, including an RBI single, to continue his hot hitting at home. Brad Miller also added an RBI single as Seattle won for the sixth time in seven games.
Seager is hitting .613 in his past eight home games.
Fernando Rodney worked the ninth for his 22nd save. Nick Swisher singled and scored on Michael Bourn's two-out single, but Rodney got Asdrubal Cabrera to pop up for the final out.
Chavez led off the first with an infield single and stole second base with two outs. Seager then dumped a single into center and Chavez was able to score standing up.
The Mariners scored in almost the same way in the fourth. Michael Saunders singled with two outs and advanced to second on a wild pitch before Miller looped a base hit to center for a 2-1 lead.
Chavez provided some cushion with the 29th homer of his career.
It was the third straight start in which Bauer (2-4) pitched into the seventh, but he has not finished that inning this season. He threw 111 pitches, below his season high of 119, and gave up nine hits while striking out five.
Young (7-4) was done after five innings despite giving up just four hits and one run. The Indians made him work deep into counts and his pitch count was at 91 after five innings.
Joe Beimel tossed a perfect sixth and Danny Farquhar was solid in the seventh, although the Indians missed a chance to keep the inning alive because of a poor baserunning decision. With two outs, first baseman Logan Morrison booted Bourn's grounder with Swisher on first. Swisher never stopped at second, but Morrison recovered and threw him out at third.
Cleveland threatened again in the eighth on a two-out walk by Carlos Santana and a double from Jason Kipnis. Charlie Furbush got Lonnie Chisenhall to ground out, ending the inning.
NOTES: Seattle's bullpen has allowed two earned runs in the past 24 innings. ... Cleveland plans to start LHP T.J. House in Sunday's series finale. House still must be recalled from the minors. ... The Indians hope RHP Justin Masterson, scratched from Sunday's start with a sore knee, will be able to go Tuesday in Los Angeles against the Dodgers.