In one of the most unique circumstances ever for a no-hitter, Alvarez (5-6) held the American League Central champion Tigers hitless through the top of the ninth of a scoreless interleague game.
But the 23-year-old Venezuelan had to wait to celebrate the Marlins' fifth franchise no-hitter until Miami loaded the bases with two out in the bottom of ninth.
Stanton began the rally with a one-out single against Luke Putkonen (1-3), went to second on a Logan Morrison hit advanced to third on a wild pitch.
With pinch-hitter Greg Dobbs at the plate, Putkonen uncorked another errant throw, allowing Stanton to race home with the game-winning run.
Alvarez issued just one walk and struck out four and also made two sparkling ninth-inning fielding plays as the Marlins finished a disappointing 62-100 season with a memorable win.
Justin Verlander tossed six innings of shutout ball for the Detroit, scattering three hits with a walk while striking out 10.
The Tigers enter the AL playoffs after finishing with a 93-69 mark.