Rodriguez's knock on the doorstep of the 600-homer club came in the seventh inning off reliever Robinson Tejeda, who grooved a 0-2 fastball that A-Rod dispatched over the right-field wall for his 16th home run of the season.
A-Rod had the option of trotting, but Jeter didn't in the third, smashing a drive toward the New York bullpen that eluded David DeJesus when the center fielder crashed into the plexiglass fence and suffered a right thumb sprain.
Jeter slid home safely ahead of a relay throw with his first inside-the-parker since Aug. 2, 1996, off Kansas City's Jeff Montgomery, when Girardi was on base to take part in the play.
"You probably won't see another one for a while," Jeter said. "When I hit it, I hit it well. And then I saw [DeJesus] sort of timing his jump. He made a great play on it, but fortunately -- for us and for me -- the wall knocked it out."
Sabathia (13-3) needed all the help he could get while venturing 120 pitches into an up-and-down effort, scattering 11 hits but avoiding the majority of damage while exiting charged with four runs (three earned).
"He was able to pretty much shut the door after the second inning," Girardi said. "He had given up seven hits in the first two innings. That's a lot of hits for CC. He found a way to get it done tonight and that's the mark of a good pitcher."
Sabathia walked four and struck out nine in the effort, and said his changeup and fastball command was betraying him, especially early.
"A win is a win," Jeter said. "You're not going to always go out there and shut teams down. You're not going to always go out there and score 10 runs. You're going to have to battle. CC didn't have his best stuff, but he gave us an opportunity to win and our bullpen did a good job."
"We gave ourselves opportunities to score runs," said Kansas City's Willie Bloomquist. "When you do that against a guy like CC, that's all you can ask for. He gets tougher when guys get on base. It's tough to come up with a key hit off a guy like that."
The Royals notched two quick runs in the first against Sabathia, as Jose Guillen stroked a RBI double and Wilson Betemit added a run-scoring single.
But the Yankees should have had an inkling about the night to come when they caught a break, as Betemit was thrown out at second base stretching before Guillen could touch the plate, with home-plate umpire Eric Cooper immediately looking toward the press level to wave off the run.
Scott Podsednik added an RBI single in the second inning that tipped a diving Jeter's glove, and Kansas City moved across its fourth run in odd fashion come the sixth, as Sabathia struck out Yuniesky Betancourt on a pitch in the dirt. Catcher Jorge Posada saw Bloomquist dancing off third and fired an errant throw down the left-field line.
"At times, as players, we're going to make reads that are incorrect," Girardi said. "His idea is to hold the guy there. Obviously he saw a bigger lead than maybe there was."
A-Rod made the first strike against Kansas City starter Bruce Chen, looping a two-run ground-rule double inside the right-field line in the first inning.
"Tonight we needed every run because they swing the bats really well," Rodriguez said."
Posada had an RBI double in the fifth and Marcus Thames added a sacrifice fly against the journeyman Chen, who allowed five runs in six innings.
Mark Teixeira also improved to 9-for-14 (.643) in his career against Chen, who should have considered himself fortunate that Teixeira did not improve on the career six homers against him.
"It's probably just one of those statistical anomalies," Teixeira said. "There's probably a lot of guys I should hit and I'm 0-fer against. I just seem to always face him when I'm hitting well."
With Sabathia leaving two runners aboard in the seventh, the Yankees needed a big outing from Dave Robertson, who induced a popout and recorded a heart-skipping strikeout in the dirt on Bloomquist, as Posada lobbed the toss wildly and forced Teixeira to leap before running to the bag.
Joba Chamberlain kept the blood pressure up in the eighth, creating a bases-loaded, two-out jam -- helped by a missed call at third base where Podsednik was called safe on a steal attempt -- but escaped by inducing the fielder's choice that preceded New York's four-run eighth to blow the game open.
"You're going to have those games," Girardi said. "You're not going to play an error-free game every night, you're not going to pitch a perfect game every night. You've got to find ways to win games in different manners."