Verlander (3-2) pitched a two-hitter for the third shutout and fourth complete game of his career to improve to 2-7 at Progressive Field and 6-10 overall against the Indians.
The Tigers scored in the eighth off Lee (1-5) when second baseman Luis Valbuena couldn't get the ball out of his glove in time to get the third out of the inning.
Granderson walked with one out, stole second and went to third on a groundout by Placido Polanco. Clete Thomas then hit a slow grounder that Valbuena fielded, but double-clutched on the throw. Thomas hustled down the line to beat the throw for an RBI single.
Verlander allowed Victor Martinez's double with one out in the seventh and Asdrubal Cabrera's one-out single in the first, but Cabrera was thrown out trying to stretch it to a double. He also walked two: Valbuena in the third and the ninth.
After giving up the leadoff walk in the ninth, Verlander fielded a bunt by Kelly Shoppach and threw out Valbuena at second. Grady Sizemore, in a 3-for-23 slump, then hit a fastball to center that Granderson caught with a leap, his glove extending over the wall.
Verlander finished it off by fanning Cabrera.
Detroit made several good defensive plays to back Verlander. Shortstop Adam Everett made a diving backhand stop of a line drive by Shin-Soo Choo and easily doubled Martinez off second to end the seventh. In the fifth, left fielder Ryan Raburn made a diving catch of a sinking liner by Ben Francisco.
Otherwise, Verlander was in complete command for the second straight game against Cleveland. He had allowed one run and two hits with 11 strikeouts over seven innings in a 3-1 win over the Indians and Lee in Detroit on Sunday.
After yielding 24 runs in 21 innings over his first four starts, Verlander has given up two runs while striking out 31 in 23 innings in winning his last three.
