Corey Kluber's day was already done when Cleveland scored a run in the seventh inning to make him the pitcher of record.
Then the Indians had to sweat out Detroit's ninth-inning rally before the right-hander could celebrate his first career victory.
"It's nice to get the first one out of the way," Kluber said. "Took a little while — longer than I would have liked — but, yeah, it's a great feeling."
Asdrubal Cabrera's tiebreaking sacrifice fly in the seventh lifted the Indians to a 3-2 win over the Tigers on Monday. Kluber went six innings and got the victory, and Vinnie Pestano held on for the save.
Pestano allowed two baserunners in the ninth but escaped for his second save of the year. Prince Fielder doubled but was unable to move to third on Delmon Young's tapper. Brennan Boesch was hit by a pitch, but he and Fielder were stranded when Jhonny Peralta struck out and Avila hit a grounder between first and second.
Avila's hit nearly went through, but second baseman Jason Kipnis ranged to his left, fielded the ball and threw to Pestano covering first.
"That's one that people think gets monotonous in spring training because you work on that every single day," Cleveland manager Manny Acta said. "But it takes repetition to get it done right, and Jason Kipnis deserves a lot of credit. That was a tremendous play."
Detroit entered the day tied for first in the AL Central. The game was tied at 2 in the seventh when reliever Darin Downs (1-1) allowed two singles and a walk to load the bases with one out. Cabrera then lifted a fly to center off Brayan Villarreal.
Kluber (1-3) allowed two runs and six hits in his seventh career start. He struck out four and walked one.
"He's got good stuff — big, strong kid, throws hard, has a lot of movement," Avila said. "Just did a really good job today of mixing it up, keeping everybody off balance and just kind of limiting those mistakes and making a pitch when he needed to."
Detroit starter Anibal Sanchez allowed two unearned runs in six innings.
The Tigers were coming off a three-game sweep of Chicago that pulled them even with the White Sox atop the division. They were sloppy early on in this one, allowing unearned runs in the first and third. Avila's two-out passed ball allowed Cleveland to open the scoring, and a throwing error by Avila put a man on third two innings later.
Detroit brought the infield in, and Cabrera singled up the middle.
The Tigers scored in the first on a single by Young and in the fourth on a single by Peralta. With men on first and second and nobody out in the fourth, Avila hit into a double play, enabling Kluber to limit the damage.
Detroit fell a half-game behind the White Sox, who were playing later against Minnesota.
Kluber pitched briefly for the Indians last year and was knocked around in his first three starts of 2012. But in his last four, he's allowed six earned runs in 22 innings, striking out 19 and walking six.
Cody Allen pitched the seventh for Cleveland, and Esmil Rogers worked the eighth. Detroit's Andy Dirks hit a deep fly to center in the eighth that was caught, and third baseman Brent Lillibridge made a diving stop on Miguel Cabrera's grounder.
NOTES: Downs had pitched only 15 2-3 innings in his career before this game, although he came in with a 1.72 ERA. ... Detroit RHP Rick Porcello (9-10) faces Cleveland RHP Justin Masterson (10-12) on Tuesday night.