The Central Division-leading Tigers have won three straight, matching a season high.
New York has lost a season-high four in a row, equaling the most consecutive losses it had last season.
Verlander (1-2) pitched seven-plus scoreless innings, allowing seven hits and no walks and resembled the rising star he was in his first two seasons, not the pitcher who struggled last year and in his first four starts this season.
Sabathia (1-2) gave up four runs on six hits in another disappointing performance for the pitcher the Yankees gave a $161 million, seven-year contract last winter. He did, though, pitch his 27th career complete game and first with the Yankees. He pitched 10 last year with Cleveland and Milwaukee.
Detroit got to Sabathia right away with two hits in the first inning, including Miguel Cabrera's RBI single.
Sabathia was solid over the next four innings before allowing Curtis Granderson's bunt single, which he struggled to cover, Placido Polanco's double and Ordonez's two-run homer that bounced off the top of the right-field wall.
Verlander gave up a pair of singles to start the eighth and was replaced by Bobby Seay, who got out of the jam by getting Johnny Damon to pop up, Mark Teixeira to hit a fly to the warning track and striking out Hideki Matsui.
Fernando Rodney entered in the ninth and after giving up three straight hits, including Nick Swisher's RBI single, he got bailed out by third baseman Brabdon Inge. Inge charged across the infield to start up a double play on pinch-hitter Jorge Posada's grounder that scored a second run.
Rodney finished off the Yankees by getting Ramiro Pena to pop out, improving Detroit's home record to 5-1.
Notes: Derek Jeter's first at-bat surpassed Mickey Mantle's Yankees record of 8,102. ... Michigan State basketball coach Tom Izzo threw out the first pitch. ... Yankees 2B Robinson Cano extended his hitting streak to 14 games.
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