After Alvarez finished off the ninth with the game scoreless, he had to wait to see if it would become an official no-hitter. A Major League Baseball ruling in 1991 said only complete games of nine or more innings with no hits would count.
The Marlins loaded the bases and with pinch-hitter Greg Dobbs at bat, Luke Putkonen threw a wild pitch that let Giancarlo Stanton score. Alvarez was on deck, and he took off his batting helmet and started to celebrate while still wearing his batting gloves.
Later, Alvarez went into the stands to hug his pregnant wife and kiss her belly.
Alvarez (5-6) struck out four, walked one and hit a batter against a patchwork Tigers lineup on the last day of the season.
It was the third no-hitter of the year, joining those by Homer Bailey of Cincinnati and Tim Lincecum of San Francisco. Alvarez.
The 23-year-old righty from Venezuela capped off a dismal season for the Marlins in which they finished at 62-100.
Alvarez pitched the first season-ending no-hitter since Mike Witt of the Angels threw a perfect game at Texas in 1984.
With the Tigers' playoff slot settled, they rested four starters and had pulled three others by the seventh inning. Miguel Cabrera, who won his third consecutive batting title, never stepped to the plate.
Twice the Tigers were robbed of hits by fine defensive plays, including Alvarez's leaping snare of Don Kelly's one-hopper before he threw to first for the second out in the ninth.
Alvarez struck out Matt Tuiasosopo on a 3-2 pitch - his 99th - to end the top of the ninth. Then he needed the help from the Marlins' offense, which is last in the majors in runs and the main reason they finished with the worst record in the NL.
Stanton singled with one out in the bottom of the ninth against Putkonen (1-3) and took second on a single by Logan Morrison. Both runners advanced on a wild pitch, and they held as Adeiny Hechavarria grounded out to the shortstop.
After Chris Coghlan walked to load the bases, Putknonen's first pitch to Dobbs was a low inside breaking ball that escaped catcher Brayan Pena. Stanton scored standing up with his arms raised, and the Marlins mobbed Alvarez near home plate.
Then, at last, Alvarez had his no-hitter, the fifth in Marlins' history.
Baseball appointed an eight-man committee on statistical accuracy in 1991 that defined no-hitters. That dropped 50 disputed games from the no-hit list.
Alvarez, acquired by the Marlins in a blockbuster trade with Toronto last November, lowered his final ERA to 3.59. His only previous complete game was May 4, 2012, a six-hit shutout for the Blue Jays against the Angels. He hadn't pitched more than 7 1-3 innings this season.
The Tigers' postseason assignment was determined before the weekend, and they'll start a division series at Oakland on Friday. Prior to the game, Tigers manager Jim Leyland acknowledged he and his players were already thinking ahead.
"I want to play this game, I want to win this game, but I want to get this over with and get home," Leyland said. "Guys are anxious. They want to get to the postseason."
The Tigers came close to a hit several times. Shortstop Hechavarria caught Ramon Santiago's liner in the third with an acrobatic leap. Detroit pitcher Justin Verlander, who is 0 for 27 lifetime, hit a drive to right field that landed foul by a couple of feet in the sixth inning.
Alvarez hit Prince Fielder in the back with a breaking pitch with two out in the first inning, then retired 12 batters in a row before Jose Iglesias reached on an error by Hechavarria in the fifth.
Alvarez retired another 12 in a row before he walked Andy Dirks on four pitches with two out in the ninth.
Verlander struck out 10 in six scoreless innings in his final tuneup for the playoffs. He finished with an ERA of 3.46.
Doug Fister, part of Detroit's playoff rotation, pitched a scoreless seventh. Rick Porcello, a starter moved to the bullpen for the playoffs, followed with a perfect eighth.
The previous pitcher to throw a no-hitter in the Marlins' 21-year history was Anibal Sanchez - now with the Tigers - who did it in 2006 against Arizona.
The last time the Tigers were no-hit was July 26, 2010, when Tampa Bay's Matt Garza beat them 5-0.
NOTES: Marlins 2B Donovan Solano was held out of the lineup but said he felt fine less than 24 hours after being hit in the helmet by a 95 mph fastball. ... Tigers pitchers had 13 strikeouts Sunday and finished with 1,428 this season, a major league record. ... The crowd of 28,315 pushed Miami's final attendance total to 1,586,322. Playing in a ballpark that opened last year, they had the second-worst average attendance in the majors, ahead of only Tampa Bay.