Lee (8-3) scattered nine hits, walked only one and struck out 11 to post a win in his fourth straight start.
With his latest fine performance, Lee, rumored to be on the trading block, lowered his earned run average to 2.34, the best in the American League.
Branyan's third-inning, three-run clout erased an early 1-0 Detroit lead and put the M's ahead for good. Kotchman launched his own three-run shot in the fifth and went 3-for-3 as the Mariners salvaged one contest of a three-game set at Comerica Park.
Tigers starter Jeremy Bonderman (4-6) was rocked for seven runs on nine hits over five innings.