NEW YORK -- David Price gave his new team a chance to win. Later, his catcher delivered the deciding stroke.
"Happy it's over, and happy we won," Price said. "Finally feel part of the team."
Price pitched 8 2/3 innings and left with the score 3-all.
The AL Central leaders got Price from Tampa Bay the past Thursday in a three-team deal minutes before the tradeg deadline. The lefty ace got to keep his No. 14; center fielder Austin Jackson, who wore it with the Tigers, was sent to Seattle in the swap. Price leads the majors in strikeouts (199) and innings (179 1/3).
"He really looked exactly like he did in Tampa, except he had the Tiger uniform," manager Brad Ausmus said.
Bushy bearded Joba Chamberlain relieved Price, and the crowd booed the formerly clean-shaven, former Yankees reliever.
"I was a little worried about him being amped up -- being in New York," Ausmus said.
Chamberlain got four outs without permitting a hit.
"I didn't know what to expect," he said. "I definitely had to take a couple of deep breaths."
Avila homered with one out off Matt Daley (0-1). Joakim Soria (2-4) got the win. Joe Nathan earned his 23rd save in 28 tries by retiring Chase Headley on a leadoff drive that was caught at the right-field wall.
"Two strikes, you know, you're not taking a full-blown normal swing," Headley said. "But yeah, I felt I got enough of it that it had a chance. Unfortunately, it came up just short."
This was the Yankees' 16th straight game decided by two or fewer runs. They're 9-7 in that span. It's the longest such streak in the majors since a 16-game stretch by Baltimore in 1975, the team said in citing the Elias Sports Bureau.
"You always think the worst," he said with his hand bandaged. "I thought it was broke."
The Tigers tied it at 3 in the seventh, helped by some smart swinging by Victor Martinez. The cleanup man led off by hitting an easy grounder to the uncovered left side of the Yankees' over-shifted infield for a single, then scored on a two-out single by Avila. Andrew Romine homered in the Detroit sixth.
Tigers: Shortstop Eugenio Suarez didn't play the day after spraining his left knee while sliding into second base on a steal. Ausmus said there's a chance Suarez could play Wednesday.
Yankees: First baseman Mark Teixeira went 0-for-5. He was a late scratch Monday because he felt lightheaded. ... Left-hander CC Sabathia says doctors took out a bone chip they found in his knee when they did season-ending surgery last week. He'll soon get a stem-cell injection. He expects to ready for spring training.
Verlander (10-9, 4.66 ERA) starts against Chris Capuano (1-2, 4.50 ERA). Verlander is 0-2 in five regular-season starts at the new Yankee Stadium. There's no telling if his special fan will be in the stands -- Verlander flipped a ball to supermodel Kate Upton on Monday night, but she wasn't sitting in her seat behind the Tigers dugout Tuesday.
JOBA THE BEARD
Yankees manager Joe Girardi got a good look at Chamberlain and said "his beard is quite large." Girardi said he asked Chamberlain if he's ever found anything hidden in the bushy growth and the pitcher told him: "Sometimes, guys try to sneak seeds in there."
With a runner on second and one out in the seventh, Brendan Ryan hit a soft liner that Kinsler caught. Kinsler pivoted and tried to throw to second for a double play but slipped and tossed the ball straight into the ground. Fortunately for the Tigers, it went right to first baseman Miguel Cabrera.