Lindor singled in the first inning when Cleveland scored three times, doubled and scored in the third and homered in the fifth as the Indians ended Detroit's five-game winning streak.
Lindor, who finished second in last season's AL Rookie of the Year voting, also made an outstanding defensive play at shortstop in the second inning.
Josh Tomlin (4-0) remained unbeaten in four starts, allowing two runs in six innings.
Verlander (2-3) gave up seven runs in five innings.
The Indians beat the Tigers for the fourth straight time this season. Cleveland swept a three-game series at Comerica Park on April 22-24.
Michael Brantley, playing his first game at Progressive Field following shoulder surgery in November, had an RBI single in the third.
Lindor took a hit away from Justin Upton with a diving stop at deep short, got to his feet and made a strong throw to first.
Ian Kinsler hit a two-run homer in the fifth for Detroit.
Tomlin scattered nine hits, struck out five and didn't walk a batter.
Verlander allowed eight hits, struck out three and walked two. He fell to 18-20 in 45 career starts against Cleveland. The right-hander is 9-14 in 24 career starts at Progressive Field.
Nick Castellanos, who leads the league with a .368 average, had two hits, including an RBI single in the eighth.
Upton singled with one out in the fourth, but was picked off first by Gomes.