Raul Ibanez singled to center, giving the Yankees a 1-0 lead.
The Yankees made it 2-0 in the sixth when Ichiro Suzuki doubled in Jeter, who scored from first after drawing a walk.
Granderson, who entered the game 1-for-16 with nine strikeouts, put the Yankees up 3-0 in the seventh with a homer to right, his second hit of the game. Girardi had decided not to bench his struggling center fielder, but did sit Rodriguez, and also did not commit to returning him to the lineup in the ALCS, after Friday's game.
The benching of the Yankees' $29 million man raised eyebrows, but Girardi said he could only worry about the present with his team on the cusp of elimination. So he started lefties Eric Chavez at third base and Ibanez at DH against the right-handed Hammel.
Rodriguez, 2-for-16 with nine strikeouts in the series, said he had to "look in the mirror" and didn't blame his manager for the humbling move.
"Obviously I'm not happy and, you know, I was disappointed," Rodriguez said before the game. "But I keep telling you guys, this is not a story about one person, this is about a team."
Rodriguez, who was not called on to pinch hit against a left-handed pitcher in the seventh, did not speak to reporters after the game.
Notes: Right-handed hitter Lew Ford started as the DH for the Orioles instead of future Hall of Fame candidate Jim Thome against lefty Sabathia. Manager Buck Showalter said he didn't want to "overextend" Thome physically and liked having him as a pinch-hitting option. ... Girardi said he would sort out his rotation past Pettitte in the next couple of days, and address his lineup Saturday.