The Tigers went into the final weekend with a two-game lead over Minnesota, but got off to a bad start when Scott Podsednik hit a leadoff home run.
Detroit lost for the fourth time in six games, all while the Twins were taking a big lead against Kansas City.
Peavy (3-0) pitched eight scoreless innings and Carlos Quentin also homered. Out for three months because of an injured right ankle, Peavy gave up just two hits and showed the form he had as the 2007 NL Cy Young winner.
Edwin Jackson (13-9) gave up a career-high eight runs.
If the Tigers fail to hold off Minnesota, they will become the first team in major league history to lead a division on May 10 and stay atop it until losing the title in the last week of a season.
Detroit still has an opportunity, though, to win the AL Central without any help from the last-place Royals. With a magic number of two, the Tigers can wrap up the division by beating the White Sox the next two days.
The Tigers are set to start Alfredo Figaro (2-1) on Saturday night against Freddy Garcia (2-4) and the White Sox.
If they need to win Sunday to clinch the division, the Tigers plan to put Justin Verlander (18-9) on the mound against John Danks (13-10).
In the series opener against the White Sox, it didn't look good for Detroit early _ or late.
Podsednik sent Jackson's third pitch into the right-field seats for just his sixth homer of the year and his first to lead off a game since 2004. Detroit had its best hitter, Miguel Cabrera, at the plate in the first with two on and one out and Peavy struck him out and got Aubrey Huff to fly out.
After Placido Polanco hit a one-out single against Peavy in the first, Detroit didn't get a base hit off him until Al Avila singled to lead off the eighth.
Jackson, who lately has not looked like the All-Star he was at midseason, let the game get out of reach in the sixth.
Gordon Beckham drew a leadoff walk, A.J. Pierzynski followed with a single and walks to Paul Konerko and Jermaine Dye forced home a run. Mark Kotsay chased Jackson with a two-run double and Quentin _ the first batter to face Casey Fien _ hit an RBI single. Alexei Ramirez's sacrifice fly made it 8-0.
NOTES: Peavy threw seven scoreless innings last week against Detroit. ... Magglio Ordonez extended his hitting streak to 10 games.