New York did not allow Crosby -- who was trying to become just the fourth lefty in the last 30 years to beat the Yankees in his big league debut -- to finish the fourth inning, though he surrendered just four hits on the night.
It was Crosby's command that was his undoing, as the patient New York hitters worked him for four bases on balls -- all in a five-run second inning -- on the night.
After walking three hitters already in that pivotal second frame, Crosby issued a two-out pass to Derek Jeter, plating the Yankees' first run of the game. Curtis Granderson, the next batter, made it count with his fourth grand slam of his career and 17th long ball of the season -- a shot that carried over the right-field wall just inside the foul pole.
"He came after me the first at-bat with fastballs, and I wasn't able to catch up to it, so I figured they'd probably stay with it," Granderson said. "At the same time, he threw a lot of offspeed stuff to [Robinson Cano] his first at-bat, but I just wanted to be ready to hit, and if he did do it, I didn't want to miss it like I did the first time."
New York suddenly had a 5-1 lead, and it was enough for New York's ace to keep the Tigers at bay. Sabathia, who has now turned in a quality start in six of his last seven outings, surrendered three earned runs while scattering eight hits over seven frames and striking out five.
"To get us through 7, you look up and he's at 70 pitches through three innings," Yankees manager Joe Girardi said. "Similar to what he did in Oakland, he really seemed to find his rhythm after."
Sabathia did labor through the first three, facing 16 hitters in that span, but said he was able to make an adjustment with his fastball command to right the ship.
"It's tough, but you've got to go out and battle," he said of the early struggles. "I felt like that's what it was today -- it was a battle. Just trying to make pitches and was able to get a win. These guys scored some runs, made some great plays and we got a win."
Sabathia has now beaten the Tigers twice this season, and helped New York to just its third win in nine games at Comerica Park over the last two seasons.
Quintin Berry -- who finished the night a home run shy of the cycle -- scored two of Detroit's three runs off Sabathia, tripling in the first inning and doubling in the third before coming around to score. Ramon Santiago also homered in the third, and Miguel Cabrera doubled and scored in the eighth.
After adding solo runs in the sixth and eighth, Alex Rodriguez helped seal the deal for New York with a two-out, two-run homer in the top of the ninth off Detroit reliever Octavio Dotel.
Meanwhile, Crosby joins Kansas City's Will Smith and Baltimore's Wei-Yin Chen as the other rookies who have fallen to the Yankees in their Major League debut this season.
"When you bring somebody up, you're prepared for anything as a manager," Tigers manager Jim Leyland said. "And I was prepared for exactly what happened tonight. I was also prepared for if he gets on a roll and gets some confidence going, he might shut them down pretty good. That's just the way it happened. It was one of those scenarios that was a possibility, and it was a scenario that happened. He just lost his control. We talked about it before the game: The Yankees don't swing at pitches that [teams] swing at in Triple-A."
The pitches that Granderson and Rodriguez swung at -- and connected on -- in the zone helped the Yankees forget for a day their recent troubles with men in scoring position. They entered the game 21-for-138 (.152) in such situations since May 13.
"It's always important for us," Girardi said of Friday's surge. "Because you need to score runs and you know what the Tigers are capable of doing that. I thought our guys did a pretty nice job with Crosby. They worked some walks on him and made him throw some pitches, and Curtis made him pay."