The Yankees trailed 3-1 entering the bottom of the ninth inning. Didi Gregorius reached first base on a fielding error, before Giancarlo Stanton singled in the next at-bat. Sanchez then stepped to the plate to face Twins closer Fernando Rodney.
The right-handed reliever threw a 94.9-mph two-seam fastball for a strike with his first offering. He then tossed in a 96.5-mph four-seam fastball. Sanchez crushed the pitch deep to left field, just inside the foul pole.
The catcher received a Gatorade bath after the shot.
Sanchez went 1-for-4 on the day with 3 RBIs and a strikeout.
"This definitely is up there, definitely a very exciting moment," Sanchez told reporters. "The other special moment was when we made it to the playoffs, but this is up there."
Sanchez is now hitting .202 on the season with six home runs and 21 RBIs. The Yankees start a three-game series against the Los Angeles Angels at 10:07 p.m. Friday at Angel Stadium of Anaheim in Anaheim, Calif.