Sanchez was heading towards a second career no-hitter with one out in the ninth inning before Joe Mauer punched a single up the middle to deny the Venezuelan a chance to become the 28th pitcher in Major League history with multiple no-hitters.
The win catapulted the Tigers (27-19) back to the top of the American League Central, in front of the Cleveland Indians (27-20), while Minnesota (18-27) remain rooted to the bottom.
Detroit's charge up the standings was aided by Boston's John Lackey, who also pitched an impressive game to lead the Red Sox to an 8-1 victory over the Indians.
Lackey allowed just two hits and one unearned run over seven innings, striking out eight, while Mike Carp helped the offence with a three-run homer in the second.
Boston improved to 29-20 to keep pace with the Yankees (29-18) in the American League East after the Bronx Bombers proved too strong for Tampa Bay (24-23) in a 9-4 win.
However, it was not all good news for the Yankees, who lost Curtis Granderson and pitcher David Phelps to injuries after both were struck by fast-moving balls.
Granderson suffered a hand fracture and will be sidelined for at least a month while Phelps has some bad bruising but should be on the mound for his next scheduled start.
In the National League, World Series champions San Francisco fell out of a three-way tie at the top of the West division with a 5-0 loss to Colorado, who remain level with Arizona after the Diamondbacks beat San Diego (21-26) 5-2.
The Rockies and Diamondbacks improved to 27-21 while the Giants slipped back to 26-22 with the loss.
Washington pitcher Jordan Zimmermann grabbed an eighth win of the season as his Nationals (25-23) took down Philadelphia (23-25) 5-2.
(Reporting by Ben Everill in Del Mar, California; Editing by John O'Brien)
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