Under scrutiny all season, the 36-year-old Jeter had four hits, three RBIs, and his first stolen base of the year while raising his batting average from .256 to .276.
Granderson followed Jeter's second homer with his AL-leading 11th of the season.
Francisco Cervelli hit a grand slam and Mark Teixeira added two-run shot in the eighth, a six-run outburst off rookie Cody Eppley that began with an umpire's apparent missed call.
Sabathia (3-2) pitched into the seventh with a season-low two strikeouts while matching a season high with four walks, all of those in the first four innings. The big lefthander gave up five runs, three earned, and five hits.
The Yankees, who had lost four of five, overcame an early 4-0 deficit to end a stretch of 16 games in 16 days with a 9-7 record.
The Yankees were ahead by 6-5 when Nick Swisher started the eighth with a grounder to Mike Napoli, and the first baseman slid his foot toward the side of the bag.
But first-base umpire Andy Fletcher ruled that Napoli never touched the bag. Napoli threw his hands up in disbelief and manager Ron Washington came out for a heated argument.
Television replays appeared to show that Napoli touched the bag before Swisher got there.
Jorge Posada and Brett Gardner followed with singles before Cervelli's first career slam, his first homer in the majors since June 24, 2009. Teixeira later added his ninth homer of the season.
Yankees 12, Rangers 5
New York 002 020 260 – 12 16 4
Texas 310 000 100 – 5 8 1
New York AB R H BI BB SO Avg.
Jeter ss 6 2 4 3 0 0 .276
Granderson cf 4 3 3 2 1 0 .283
Teixeira 1b 5 1 2 2 0 1 .259
Al.Rodriguez 3b 4 0 1 1 0 0 .263
Cano 2b 4 0 0 0 1 0 .290
