Alvarez (1-2) retired the first 15 batters en route to the third complete game of his career. He struck out four, walked none and threw 90 pitches.
He also had a two-out RBI single in the sixth to make it 3-0.
The Mariners lost their fifth game in a row and were shut out for the fourth time.
Marcell Ozuna had a three-run homer, his third, and an RBI single to hike his average to .343. Adeiny Hechavarria contributed three hits, scored twice and made two fine plays at shortstop. Christian Yelich doubled to extend his hitting streak to 13 games.
Rookie Roenis Elias (1-2) allowed six runs in 5 2-3 innings.
The Mariners had eight left-handers in the lineup against Alvarez, but that didn't faze the right-hander, who retired the side in order for five innings before Dustin Ackley singled to shallow left-center on the first pitch of the sixth.
After the crowd of 24,003 gave Alvarez a warm ovation, Ackley was erased on a double play. Zunino doubled with one out in the ninth for the Mariners' other hit.
Alvarez, who turned 24 Friday, reached 96 mph on the scoreboard radar gun and had good command of his breaking pitches. He went to three balls on only one batter.
The dominating performance was reminiscent of the Venezuelan's no-hitter on the final day of last season, when Miami scored in the bottom of the ninth to beat Detroit 1-0. That was the first time a no-hitter was secured with a walk-off wild pitch to bring home the winning run, and Alvarez was in the on-deck circle at the time.
The Mariners tried to pitch around Giancarlo Stanton, who beat them with a walk-off grand slam homer Friday. He walked twice, each time with a runner on base.
Casey McGehee foiled the strategy in the third when he singled home the first run after Stanton was intentionally walked.
Hechavarria singled in the fourth and scored from third on a two-out passed ball by Zunino. Hechavarria singled and scored again on Alvarez's single in the sixth, and Ozuna's homer made it 6-0.
The Marlins have homered in 10 consecutive games after finishing last in the majors in that category in 2013.
NOTES: Marlins 2B Rafael Furcal (hamstring) will begin a rehabilitation assignment Monday with Double-A Jacksonville. ... Marlins RHP Jacob Turner (shoulder) is scheduled to make his first rehab start Wednesday for Class A Jupiter. ... The Mariners' Corey Hart was given the night off. ... The Mariners' walk-off loss Friday was their 52nd since the start of the 2010, by far the most in the majors during that span. ... The Marlins became the first team since the Red Sox in 1949-52 to hit a walk-off grand slam in three consecutive seasons. ... Mariners LHP Joe Beimel turned 37 Saturday. ... Seattle RHP Brandon Maurer and Marlins RHP Kevin Slowey are scheduled to make their first starts of the season Sunday.