Curtis Granderson and Robinson Cano homered while Nick Swisher had a two-run double in support of Sabathia, who nudged past the Twins' Carl Pavano and the Rays' David Price to claim sole possession of the Junior Circuit wins lead.
The contest featured a rare power show against Sabathia, who had allowed just one homer in his last 13 starts, but the damage was limited to two solo homers -- Austin Jackson teed off on the first pitch, and Brandon Inge belted a solo shot in the seventh inning.
Otherwise, the left-hander was splendid, completing seven innings of five-hit ball, walking three and striking out nine.
"CC knows how to shut the door," Yankees manager Joe Girardi said. "When he needs to make an adjustment, he's able to do it. That's why he's been such a consistent winner over the years. He knows how to make minor adjustments."
After being baffled by the likes of Kansas City's Bryan Bullington and Detroit's Max Scherzer in consecutive losses, the Yankees were almost happy to see a familiar face like the Tigers' Justin Verlander, who was touched for three runs in five pitch-heavy innings.
Guarding a sore right elbow that affects him most when batting left-handed, Swisher opened scoring in the first inning by punching a two-run single the opposite way into left field, scoring Brett Gardner and Jeter.
"It was nice to get out there, especially against Verlander, their ace, and put some runs early on the board," Swisher said. "And CC, our horse, took care of the rest."
Granderson tacked on a solo shot in the second inning, his 12th, before Verlander held the Yankees quiet for the remainder of a five-walk, five-strikeout outing that was below par, to hear the pitcher's self-evaluation.
"This is the worst I've ever felt on the mound as a professional baseball player, bar none," Verlander said. "I feel like I was so far from where I needed to be."
And the Yankees weren't complaining with a diminished run at Verlander, picking up a much-needed victory after a break-even six-game trip to Texas and Kansas City and a series-opening loss on Monday.
"He's no fun to face," Jeter said. "We took advantage, early on it looked like he struggled with his control, but he's as tough as anyone in baseball. He throws hard, his ball moves. You really don't look forward to facing him."
But at this point, Granderson might be the exception. He is even making harder outs after hitting coach Kevin Long performed a partial revamp of his swing during the series against the Rangers, reaping rewards like his blast into the right-field seats off a former teammate.
"I'm trying to get a pitch to hit and not miss it," Granderson said. "I got one that at-bat and didn't miss that one. There's very few pitches during the course of a game that you're going to get a chance to do that with against a guy like him. That was the one."
Provided with a lead to protect, Sabathia did bump into trouble in the seventh after Inge's homer, allowing a pinch-hit single to Alex Avila that drew Girardi out of the dugout for a chat.
But even with the bullpen whirling and Sabathia at 111 pitches, Girardi liked what he heard and permitted his ace to stay in. Sabathia rewarded his trust with a swinging four-pitch strikeout of Jackson to end the inning.
"He's matured a lot as a pitcher and doesn't give in anymore," Tigers manager Jim Leyland said of Sabathia. "He's just a great pitcher overall. If you're not stingy against someone like him, you're not going to win."
Cano struck for his 22nd home run in the seventh off left-hander Daniel Schlereth, a solo blast into the right-center-field seats that was his 12th this year off a southpaw, and Ramiro Pena added a sacrifice fly for the four-run cushion.
Dave Robertson hurled the eighth inning around a single, now stringing together 17 straight scoreless appearances, and Mariano Rivera completed the last three outs, allowing a hit, in a non-save situation that seemed to carry plenty of weight.
"It was nice to see that intensity back," Swisher said. "You could feel it in the stadium. What a great win for us tonight."