Verlander (1-0), fresh off signing a five-year contract extension worth a reported $140 million, shook off freezing weather in Minnesota to subdue the Twins on three hits.
The 2011 American League Most Valuable player corralled his first win in six straight Opening Day starts for the Tigers, striking out seven while issuing a pair of walks en route to the victory.
Phil Coke tossed a scoreless ninth for the save as Detroit improved to 16-4 in its last 20 games at Target Field.
Vance Worley (0-1) absorbed the loss in his Twins debut, surrendering three runs on eight hits over six innings. He allowed one walk and struck out three.
Ryan Doumit provided Minnesota's only RBI.