NEW YORK (AP) -- 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 last Thursday in a three-team deal minutes before the trading 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 big 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 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.''
The Yankees are in the midst of facing Detroit's three Cy Young Award winners. They edged Max Scherzer on Monday, and will next see Justin Verlander on Wednesday night.
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, 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. But, yeah, I felt I got enough of it that it had a chance. Unfortunately, it came up just short,'' Headley said.
This was the Yankees' 16th straight game decided by two or fewer runs, and 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.
Tigers outfielder Torii Hunter exited with a bruised left hand after being hit by a pitch from Dellin Betances in the ninth. Hunter was listed as day-to-day.
''You always think the worst,'' he said, his hand bandaged. ''I thought it was broke.''
Brian McCann and Martin Prado hit solo home runs for the Yankees, who had won three in a row.
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' overshifted infield for a single and scored on a two-out single by Avila.
Andrew Romine homered in the Detroit sixth.
Tigers: Shortstop Eugenio Suarez didn't play, a 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 when 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. 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, saying, ''his beard is quite large.'' Girardi said he asked if Chamberlain 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.