Jeremy Bonderman pitched into the eighth inning after getting off to a rough start and Gary Sheffield had two hits for Detroit (13-15), which has won seven of nine. The $139 million Tigers opened the season with seven straight losses.
With Rodriguez sidelined by a strained right quadriceps, slumping New York managed just two hits after the first inning. The Yankees have scored just 15 runs in their last five games.
A-Rod went on the DL for the first time since July 2000 before the game and he got some company later when struggling starter Phil Hughes was placed on the injured list with a strained right oblique muscle. Hughes is 0-4 with a 9.00 ERA in six starts this year.
Longtime catcher Jorge Posada also is on the DL with an ailing throwing shoulder.
The Tigers know all about dealing with injuries - they're missing starter Dontrelle Willis, key relievers Joel Zumaya and Fernando Rodney, and catcher Vance Wilson.
Detroit should get a boost Thursday when reliever Francisco Cruceta comes off the restricted list. The Tigers cleared the way for the right-hander to join the team in New York by trading right-hander Jason Grilli to the Colorado Rockies for minor league pitcher Zachary Simons before Wednesday's game.
Cruceta, who had problems getting a work visa this spring, had a successful stint with Triple-A Toledo and could be a valuable setup man for Detroit manager Jim Leyland.
The Tigers didn't need much bullpen help Wednesday. Bonderman (2-2) allowed Jason Giambi's sacrifice fly and Melky Cabrera's RBI single in the first inning before settling into a groove. He retired 12 straight over one stretch and allowed five hits in 7 2-3 innings.
Detroit went in front for good in the fifth. Edgar Renteria singled off Andy Pettitte (3-3) with one out and Thames hit the next pitch over the wall in left-center to give the Tigers a 3-2 lead. It was Thames' second homer of the season.
Polanco hit leadoff homers in the sixth and eighth innings. He went 4-for-5 and scored two runs in Detroit's 6-4 win Tuesday night in the opener of the series matching the teams with the two highest opening-day payrolls in baseball.
Pettitte allowed five runs and seven hits in six innings. He struck out three and walked one. He was 5-0 with a 1.93 ERA in his previous five starts against Detroit at Yankee Stadium.
New York has lost five of its last seven games.
