Rodriguez was back in the New York lineup, batting sixth, after being benched for the deciding game of the division series against Baltimore on Friday. Fans gave him a standing ovation as he walked to the plate with two outs in the first. Jeter, Teixeira and Ibanez all reached on walks by Fister.
The 37-year-old third baseman hadn't hit as low as sixth since Joe Torre batted him eighth in the fourth and final game of the 2006 AL division series against the Tigers, according to STATS LLC.
Both teams were coming off difficult division series that went five games. The Tigers beat the Yankees in 2006 and again last year, both times in the division series.
Fister got the win in Game 5 last year. He got off to a wild start in this one, walking three in an inning for just the second time in his career, according to STATS LLC.
With two outs, A-Rod hit a sharp groundball that Peralta dived to his right to snare. From his knees he threw to second base to just get Ibanez sliding in.
In the second, the Yankees used three two-out singles to load the bases, including Jeter's 200th postseason hit.
Cano, who was 2 for 22 in the division series, lined a ball off Fister's pitching arm. It went on a hop to a charging Peralta, whose throw barely beat Cano to first base. Cano slammed his helmet down.
Pettitte was making his 44th postseason start. He breezed through five innings, giving up four singles, including one to Triple Crown winner Cabrera in the first.
But in the sixth, Austin Jackson led off with a soft line drive to the opposite field that went over first base and got caught up in a cutout in the stands about halfway down the right field line. Jackson raced to third for a triple. After an out, Cabrera was intentionally walked, and Fielder singled to center for a 1-0 lead. Young followed with a hit.
Teixeira reached on second baseman Omar Infante's error to start the bottom half, and Ibanez doubled, but Fister struck out the side.
New York won the season series between the teams 6-4.