Alex Rodriguez played at home for the first time this season while going hitless in four at-bats and Mariano Rivera blew his second straight save opportunity. Nevertheless, the Yankees eventually prevailed to bring a halt to the Tigers' longest win streak in 79 years.
Nix drew a leadoff walk against Al Albuquerque (2-3) in the 10th, went to second on a single by Curtis Granderson and reached third on a wild pitch.
Nix was still on third with two out when Gardner singled to left on an 0-1 pitch.
New York took a 3-1 lead into the ninth before Rivera gave up a two-run, two-out homer to Miguel Cabrera.
Rodriguez struck out three times in his first appearance at Yankee Stadium since last year's playoffs. He is playing while appealing a 211-game suspension by Major League Baseball.
The win went to Shawn Kelley (4-1), who recorded the final out in the top of the 10th.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Man spent 15 hours in jail for plugging electric car into an outlet at a school