Starter Anibal Sanchez and relievers Al Alburquerque, Jose Veras, Drew Smyly and Joaquin Benoit combined to keep the Red Sox without a hit until Daniel Nava dumped a single to center off Benoit with one out in the bottom of the ninth.
Pinch-runner Quintin Berry stole second base but rookie Xander Bogaerts hit a towering pop-out to shortstop Jose Iglesias to end it.
The five Detroit pitchers bamboozled Boston batters in registering a total of 17 strikeouts at Fenway Park.
The only run of the game came in the sixth inning on a soft single to center off Boston starter Jon Lester by Jhonny Peralta that scored Miguel Cabrera.
Peralta, who went 3-for-4 in the game, rejoined the Tigers for the playoffs after serving a 50-game doping suspension.
Two more outs for Detroit would have registered the first combined no-hitter ever thrown in Major League Baseball's postseason.
The only previous postseason no-hitters were New York Yankee Don Larsen's perfect game in the 1956 World Series against the Brooklyn Dodgers, and Roy Halladay's no-hitter for the Philadelphia Phillies in the 2010 National League Division Series against Cincinnati.
Game Two of the series, which will produce the American League representative in the World Series, will be played on Sunday in Boston.