Marcell Ozuna belted a three-run homer off Roenis Elias and drove in four runs, and Christian Yelich extended his career-best hitting streak to 13 games. But the story of the night was Alvarez, who allowed just a single to Dustin Ackley to open the sixth inning before Zunino's hit.
In his last start, a no-decision at Philadelphia, Alvarez allowed 12 hits and wasn't able to get his sinker going. On the night of his birthday, he was with family, but also thought about what he needed to do to get back on track.
"I was with my family and friends at the apartment," Alvarez, a Venezuela native, said in Spanish. "We started celebrating and I started reflecting about how good this all is and what I need to do to get to the next level."
From the first inning, when he was bringing 95-mph fastballs and getting dip on his sinker, it was clear Alvarez was sharp.
"You can tell in the first inning, he came out and his [velocity] was up, 94-95," manager Mike Redmond said. "I think for him that was a good sign. You could just sense his intensity and the way he was executing his pitches. You could tell he was on a mission tonight. He was going to do everything he could do to win that ballgame, and he did."
Alvarez picked up his first win of the season, and the right-hander was making a push for his second no-hitter. In the final game of the 2013 season, he no-hit the Tigers.
Alvarez breezed through 28 batters on 90 pitches -- 62 for strikes. The way he was throwing had Redmond thinking about the no-hitter in the season finale.
"I thought it was pretty similar," Redmond said. "I was thinking to myself, 'Man, he's executing his pitches and getting ground balls.' When he's doing that, it really shows the type of stuff that he has. The velo was good. After that first inning, I felt like, 'Hey, he's got his good stuff tonight, and we've got a chance. We've just got to figure out a way to score some runs.'"
Alvarez turned in Miami's first complete-game shutout since his historic game against the Tigers. The Marlins, after winning 8-4 in walk-off fashion on Friday night, secured the three-game series win and improved to 8-10 on the season.
Pitching is expected to be Miami's strength, but until Saturday night, the staff has had its struggles.
"That's a huge start," catcher Jarrod Saltalamacchia said. "Last night was a great momentum boost for us, to be able to walk-off like that. Our thing [question mark] coming into the season was our offense. Pitching was not even a question. So our offense has been scoring runs, and our pitching has been struggling a little bit. We had to work together and figure out things together."
Alvarez was perfect through five innings, retiring the first 15 batters he faced on 53 pitches. The closest Seattle came to a hit was in the top of the fourth inning when Abraham Almonte lined a drive to deep right field. But Giancarlo Stanton, in full stride, snared it near the warning track with a backhanded catch.
Seattle collected its first hit on Alvarez's 54th pitch, a sharp single to center by Ackley to lead off the sixth. But any threat of a big inning was erased when Zunino bounced into a 5-4-3 double play. Miami was ahead by two at the time.
"That wasn't the pitch I wanted to throw," Alvarez said. "It was a [sinker], a little high. I wanted to throw a changeup down. Those are things that happen during the game, and you can't change them."
Miami's offense came up big in the sixth inning, scoring four runs and knocking Elias out of the game. Adeiny Hechavarria's infield single got things going. With two outs, Alvarez delivered a broken-bat RBI single to center. Yelich walked, and Ozuna unloaded on his three-run homer, which ended Elias' night.
Yelich opened the third with a drive to deep center. The ball was misplayed off the wall by Almonte, allowing Yelich to reach third. It was officially scored a double and an error. With one out, Stanton was intentionally walked for the third time in the first two games of the series.
When teams pitch around Stanton, the Marlins are looking for others to step up. Casey McGehee did, slapping an RBI single to center.
The Marlins were opportunistic in the fourth inning, scoring their second unearned run of the game. Hechavarria singled with one out, and he moved to second on Donovan Solano's single. Alvarez's sacrifice bunt advanced the runners, and on ball four to Yelich, the pitch got away from Zunino, and the passed ball scored Hechavarria.
With run support, the question was whether Alvarez could go the distance and complete the shutout. He did so, working around the Zunino double and ending the game on Almonte's groundout to second.
"His stuff was exceptional tonight," Mariners manager Lloyd McClendon said. "He had plenty of movement and he was pounding the zone pretty good."