Detroit pulled even with Chicago with eight games to play after the White Sox lost 4-3 to Cleveland earlier in the day.
Sanchez (4-6) retired the first 11 hitters he faced and allowed only three hits. He struck out 10 and walked one.
He threw 105 pitches in his first shutout since Sept. 10, 2011, when he tossed a one-hitter for Florida at Pittsburgh.
Bruce Chen (11-13) gave up RBI singles by Prince Fielder and Delmon Young in the first inning.
The Tigers trailed the White Sox by three games on the morning of Sept. 19, but they've made up the ground and will have a chance to win a second straight division title if they can finish strongly enough.
Chen allowed two runs and 10 hits in 6 2-3 innings.
Sanchez has six quality starts in his last seven outings.
INDIANS 4, WHITE SOX 3
CHICAGO (AP) — Chicago gave Detroit an opening to tie for the AL Central lead when Gordon Beckham hit into a game-ending forceout with the potential tying run on second base in the loss to last-place Cleveland.
The Tigers took it with a 2-0 victory over Kansas City
Down 4-0, the White Sox closed when A.J. Pierzynski and Dayan Viciedo hit consecutive fifth-inning home runs off Corey Kluber (2-4) and then pulled within a run when Paul Konerko homered off Chris Perez leading off the ninth.
Perez walked two batters with two outs, and Beckham grounded to shortstop Asdrubal Cabrera, who threw to second baseman Jason Kipnis for the force.
Chicago (82-72) had held sole possession of the division lead since Sept. 3.
Francisco Liriano (6-12) allowed all four runs and seven hits in 3 2-3 innings. He is 1-2 with a 6.30 ERA in his last seven appearances.
Kluber (2-4) gave up four hits in seven innings, retiring nine of his last 10 batters. Vinnie Pestano and Perez completed the six-hitter, with Perez gaining his 37th save in 41 chances.
Russ Canzler had three hits and homered for the second straight game, putting Cleveland ahead in the second.
TWINS 5, YANKEES 4
MINNEAPOLIS (AP) — Phil Hughes ran out of gas in the seventh inning and Boone Logan couldn't hold the lead for him as New York missed a chance to go up 2 1/2 games on Baltimore.
Hughes (16-13) was strong through six innings and the Yankees took a 3-1 lead. But he left with the bases loaded and two outs in the seventh, and Logan let one run score on a wild pitch before giving up a two-run double to Denard Span that put the Twins in front.
Joe Mauer followed with his third single of the game to cap the four-run seventh, and the Twins held on to keep the Orioles, who lost to Toronto earlier Tuesday, 1 1/2 games behind New York in the AL East.
Nick Swisher homered for the third straight game, Russell Martin also went deep and Andruw Jones hit a pinch-hit solo shot off of closer Glen Perkins in the ninth inning for the Yankees. But Perkins struck out Jayson Nix for his 15th save.
Martin's soaring shot in the seventh off Casey Fien (2-1) was his 19th this season, which ties a career high, and gave New York a 3-1 lead. ___
BLUE JAYS 4, ORIOLES 0
BALTIMORE (AP) — Aaron Laffey and five relievers combined on a six-hitter as Toronto beat Baltimore for the second straight game.
Laffey (4-6) allowed five singles in 5 2-3 innings and won his first game since Aug. 5. He had been winless in his previous six starts. He neither walked nor struck out a batter.
Baltimore remained 1 1-2 games behind first-place New York in the AL East. The Yankees lost 5-4 at Minnesota.
The Orioles had won seven of their previous nine. They had not been shut out since Aug. 3.
Joe Saunders (2-3) pitched 6 1-3 innings, allowing four runs — three earned — and 11 hits. He struck out two and walked none.
RAYS 5, RED SOX 2
BOSTON (AP) — David Price struck out a season-high 13 and Jeff Keppinger hit a three-run homer as Tampa Bay extending its winning streak to six games and kept its playoff hopes alive.
Tampa Bay remained three games behind Oakland for the AL's second wild-card spot. The Athletics beat Texas 3-2 in 10 innings.
The Rays got to Boston starter Clay Buchholz (11-7) quickly on Keppinger's three-run homer in the second and Price (19-5) was able to preserve the lead despite balking with a runner on third to pull Boston within 3-2.
Price pitched his second complete game of the season, scattering seven hits and walking none. He tied his career high with his 19th win and is scheduled for one more chance to reach 20 for the first time in his career.
Boston has lost five of six and 19 of 26.
Buchholz lasted six innings, allowing eight hits and five runs, four earned. He struck out five and walked two.
ATHLETICS 3, RANGERS 2, 10 innings
ARLINGTON, Texas (AP) — George Kottaras hit a leadoff homer in the 10th inning and Oakland moved within four games of the AL West lead by beating first-place Texas.
The A's remained two games ahead of Los Angeles for the second AL wild-card spot. The Angels beat Seattle 5-4.
Texas' magic number remained at five for clinching its third straight division crown.
Scheduled starter Yu Darvish was scratched by the Rangers about 2 1/2 hours before the first pitch because of a stiff neck. Scott Feldman took his place and allowed two runs and four hits in four-plus innings. Three relievers combined to allow one hit in five scoreless innings before Lowe gave up the decisive run.
The A's lost the opener of the four-game series 5-4 Monday night. The teams play five more times over the final eight games of the season.
Evan Scribner (1-0) earned his first career victory with a perfect 10th, and Grant Balfour got three outs for his 21st save in 23 chances.
Kottaras hit a 3-2 fastball from Mark Lowe (0-2) into the first row of the upper deck in right field. He has six home runs for the A's since he was acquired July 29 from Milwaukee.
ANGELS 5, MARINERS 4
ANAHEIM, Calif. (AP) — Zack Greinke had a season-high 13 strikeouts in five innings, and Los Angeles got home runs from Torii Hunter and Erick Aybar to remain two games behind Oakland for the second AL wild card.
According to ESPN Stats, Greinke (6-2) became the first pitcher in the live-ball era (since 1920) to strike out 13 batters in a start that lasted only five innings. Randy Johnson had 13 through his first five frames on July 4, 2001, for Arizona against Houston, but he threw one more inning.
The 20 combined strikeouts by Angels pitchers tied a major league record for a nine-inning game.
Justin Smoak homered twice for the Mariners, a solo shot in the fourth against Greinke and a two-run drive off Scott Downs during a three-run seventh that sliced the Angels' lead to 5-4.
In all, Greinke has 16 wins this season, tying his career high. The nine-year veteran has a 3.40 ERA in 12 starts since joining the Angels in a trade with Milwaukee on July 27. He was 9-2 with a 3.44 ERA in 21 starts for the Brewers.
Ernesto Frieri threw a perfect ninth for his 22nd save in 24 chances.